Aptitude - Profit and Loss - Discussion

2. 

The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is:

[A]. 15
[B]. 16
[C]. 18
[D]. 25

Answer: Option B

Explanation:

Let C.P. of each article be Re. 1 C.P. of x articles = Rs. x.

S.P. of x articles = Rs. 20.

Profit = Rs. (20 - x).

20 - x x 100 = 25
x

2000 - 100x = 25x

125x = 2000

x = 16.

Video Explanation: https://youtu.be/sidqvjUoZxY


Anshuma Chugh said: (Jul 14, 2010)  
Can you please make me understand by giving more examples?

K Soumya said: (Jul 18, 2010)  
The given solution for the problem is incorrect.

Barat said: (Jul 23, 2010)  
Answer is correct.

Pinky said: (Jul 25, 2010)  
Can you explain how SP of x articles become 20?

Sundar said: (Jul 25, 2010)  
Hi Pinky,

Please read the the question carefully and the first two lines of the explanation given, then you will understand the answer for your question.

{
The cost price of 20 articles is the same as the selling price of x articles.

Let C.P. of each article be Re. 1 C.P. of x articles = Rs. x.

S.P. of x articles = Rs. 20.
}

Have a nice guys.!

Sanjeet Kumar said: (Sep 12, 2010)  
Hi every one
here this problem is a bit difficult to understand. let me give u an another example then we will come to this.

let c.p. of 1 article is Rs. 4 and
let s.p. of 1 article is Rs. 5

now c.p. of 20 article is 20*4=80
and s.p.of 16 article is 16*5=80
the first line of the question said these r equal that is Rs. 80

now come to our problem above.
let c.p of 1 article is Rs.1
here given that c.p. of 20 article is equal to s.p. of x article

so let us calculate c.p. of 20 article=Rs 20
hence s.p. of x article is Rs. 20
so s.p. of 1 article =20/x

profit on one article= (20/x)-1
% profit=((20/x)-1)*100)/1=25

hence x=16

Sid said: (Sep 24, 2010)  
Thanks sanjeet, nice explanation.

Sarath said: (Oct 15, 2010)  
Can you explain me about the assumptions it makes me difficult to understand?

Anbu said: (Oct 23, 2010)  
Sanjeet your explanation is very good.

Aamir said: (Nov 12, 2010)  
I cant undrstnd this question plz any help me to undrstnd this

Chetan said: (Nov 12, 2010)  
Hi guys,

20 article C.P = 100rs(say)

Note: When given profit percentage, he calculates it only after selling all goods.

So 20 articles S.P = 125 (SINCE PROFIT PERCENT =25%)
now consider only S.P
125 rs --->20 articles
100 rs --->? articles
100*20/125=16

That is it simple.

Vasanthi said: (Nov 13, 2010)  
Sanjeet your explanation is very nice.

Indu said: (Nov 21, 2010)  
Very nice and simple explanation sanjeet. Thanks.

Anjali&Amp;Sandhya said: (Nov 27, 2010)  
Chetan nice answer anjali and sandhya.

Ruby said: (Dec 2, 2010)  
Sanjee how does the profit of one article will be (20/x) -1.

Chinni said: (Dec 7, 2010)  
profit=s.p-c.p
hence cost of 1 article=1
s.p of 1 article=20/x
profit=(20/x)-1

Rupesh said: (Dec 18, 2010)  
Then where is the solution of 25%.

Priya said: (Dec 21, 2010)  
How profit is given as 20-X?

Mukul said: (Dec 27, 2010)  
@priya :- when u got s.p of x article = Rs. 20 and c.p of 1 article is re.1 so for 'x' article c.p will be Rs. x .
now s.p - c.p = profit
hence 20 - x . = profit .

Parth said: (Jan 4, 2011)  
Thanx chinni and sanjeet awsum xplanation!

Vignesh.R said: (Jan 6, 2011)  
Chetan! your explanation is cute and understandable.

Jacky said: (Jan 15, 2011)  
Sanjeet kumar gives the nice explanation.

which is easly understandable.
thanks frnd.
if 25% profit given u can take the example of c.p is 4 and s.p is 5.
20*4=x*5
x=16

Sumit Yadav said: (Jan 16, 2011)  
@chetan

Its Nice. You realy did well, you make this problem very simply.

Vishal said: (Feb 1, 2011)  
priya...
in general form.
let the cost of 20 article = y rs
so cost of 1 article= y/20rs
and cost of x article = xy/20
so the profit= price-sailing price/sailing rate
25=(y-x*y/20)/(x*y/20)
by solve this u got 16 answer

Yuri said: (Feb 12, 2011)  
How we assume cp for 1 article is 1?

If we assume else then?

Habib said: (Feb 23, 2011)  
Its very very simple....

Given, CP(20 Articles)=SP(X articles)...............A

Assume, CP of 1 article is Re.1,
CP of X artilcles is rs.X..............B
CP(20 Articles)=rs.20..................C
So A becomes,
rs.20 = SP(X articles).................D

Now, Profit = SP(X articles) - CP(X articles)
= 20 - x (from B&D)

Hence find profit %, (20-x)/x * 100

Haritha said: (Mar 1, 2011)  
c.p of 20 articles= s.p of x articles .........1
s.p=((100+profit%)/100)*c.p
hence from the above values we get
s.p=(5/4)c.p
substitute in 1 we get
X=16

Prathyusha said: (Mar 2, 2011)  
Sundar and sanjeet explanation was nice!.

Good work guys!.

Thanku.

Kumar said: (Apr 12, 2011)  
How it was come by using 2000..i cant understand plz explain detaily

Pankaj said: (Apr 27, 2011)  
How to solve ( (20/x-1) x100) /25?

Kailash said: (May 1, 2011)  
Profit=x-y/y *100
25=20-y/y*100
25/100=20-y/y
1/4=20-y/y
y =4(20-y)
y =80-4y
5y =80
y =80/5
y =16
This is very shortcut method of this types questions.

Surya said: (May 17, 2011)  
Very nice explanation thanks to snnjeet.

Priyanka said: (May 24, 2011)  
How 20-x sir ?

Vivek said: (Jun 2, 2011)  
Thank for your explanation sanjeet it is so easy to understand after you explain, I like this site very much.

Roopa said: (Jun 24, 2011)  
Really nice to join your discussion.

I have simple equation;

c.p =s.p
20(Articles) = x(Articles)+profit
it means
1*20=1+.25*x
20=1.25x
20/1.25=x
20*100/125=x
16

Vinu said: (Jul 7, 2011)  
Hi kailash awesome shortcut.

Vinay said: (Aug 2, 2011)  
Please Try to Solve the Problems without any Formulas. Understand the Problem and solve it and your own.

Umesh said: (Aug 5, 2011)  
The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is:

===> LET CP BE Rs 100
CP OF 20 =2000
SP OF 20 =2000*1.25(PROFIT) = 2500
SP OF 01 =2500/20 =125
THERFORE ANSWER = 2000/125 =16

OR
CP *20 =SP *X
PUT SP=1.25CP
NOW, CP*20=1.25CP*X
CANCEL CP FROM BOTH
X = 20/1.25 =16

Nikhil said: (Aug 7, 2011)  
Awesome explanation chetan!thanx:).

Rashmi Shukla said: (Aug 19, 2011)  
Clear explanation sangeet thanks :).

Kapil said: (Aug 23, 2011)  
@Sanjeet

Why we take selling prize = 5 ?

Nj. said: (Aug 23, 2011)  
Nice Explanation Umesh!!!!! Good Job!

Vikas said: (Sep 3, 2011)  
Hi Guys,
U can use a very simple method, i.e.,
Suppose,
C.P of 1 item = Rs.100
So C.P of 20 item = Rs.2000
Now profit is 25% so,
s.p of 1 Item = Rs.125 {125% of C.P}
s.p of x Item = 2000 {= C.P of 20 Items}

Therefor number of x item = 2000/125
= 16 Ans.

Dharmendra said: (Sep 3, 2011)  
Suppose c.p. of 1 article is Rs. 1
so c.p. of x article is Rs. x.........(1)
now s.p. of x articles is 20.........from the question....(2)
now profit is s.p-c.p = 20-x .............(3)
now use the formula gain%=gain*100/c.p
25=(20-x)*100/x ...........(1)+(3)
now solve it.

Indika said: (Sep 19, 2011)  
20cp=(100-20)
20cp=80
20cp=80/4
sp=5
20cp=80/5
x=16
selling articles=16

Rinku said: (Sep 19, 2011)  
20 cp = x sp
20(cp/sp)=x
20(100/125)=x
16=x......make it simple.

Aarti said: (Sep 28, 2011)  
Simple and fair explaination jacky.

Imraz said: (Sep 29, 2011)  
Here said that cp of 20 article = sp of x article

So, 20*cp=x*sp ------(1)

Lets assume cp=100; from the question it is given that profit percentage=25%
so sp becomes 125

so the equaion 1 can be written as
20*100=x*125
x=(20*100)/125
x=16

Hanuman said: (Oct 15, 2011)  
Chetan your answer is super, thank you.

Samy said: (Nov 19, 2011)  
Thanks imraz your explanation is nice.

Phani said: (Nov 24, 2011)  
How can we convert 25%? Please tell me.

Brajesh said: (Nov 29, 2011)  
Thank you Habib for giving simple explanation.

Meenu said: (Dec 25, 2011)  
Nice Explation Habib

Preethi said: (Jan 2, 2012)  
Thank you sanjeet kumar.

Vishwam Chand said: (Jan 22, 2012)  
Chetan, Roopa, and Vikas have given the best explanations.

Shweta said: (Jan 24, 2012)  
Thanks sanjeet. Good and very clear example and explanation.

Saranya said: (Jan 28, 2012)  
I am can not understand in this problem. So please give any formulas (OR) Please give some example problems.

Pinaki Chatterjee said: (Feb 17, 2012)  
CP * 20 = SP * X,
25 % PROFIT MEANS (CP+CP*25/100)=1.25 CP
NOW YOU CAN WRITE SP= 1.25 CP,
CP*20=1.25 CP * X
X=20/1.25
X= 16

Vishnu.Pillai said: (Mar 10, 2012)  
Thanks a lot sanjeet.

Puneet Goel said: (Mar 18, 2012)  
Let c.p. IS a rs.
Then C.P. of 20 articles =20a = S.P. of x articles
So S.P. of 1 articles=(20.a)/x
So Gain=((20.a)/x)-(a)=a(20-x)/x
Now as Gain%=gain*100/C.P= ((a(20-x)/x)*100)/a=(20-x)*100/x
25=((20-x)/x)*100 => 25x=2000-100x => x=2000/125 = 16
Hence Proved :)

Riya said: (Mar 30, 2012)  
Let us assume C.P of 20 articles = Rs. 100.
Then S.P of x articles = Rs. 100.
S.P of 20 articles = Rs. 125 (as profit= 25%).
Therefore 1 article = 125/20.
x article = (125*x) /20.
Which is again equals to 100.
Hence (125*x) /20=100.
x=16.

Tannu said: (Apr 2, 2012)  
@sanjeet.

You really solve this problem in simple manner and it easy to understand. Thanks.

Abhi said: (Jun 8, 2012)  
Hii.... friends i have done this problem in this method.

Dont know whether correct or wrong.please justify me.
c.p*20=s.p*x
Gain=25%
x=?
we know s.p=(100+gain%)/100 *cp
c.p*20=125/100 *cp *x
we will cancel cp on both sides.
by solving we will get x=16.

Shine said: (Jun 24, 2012)  
Since the CP & SP are equal,

Profit%= ( (no.of items left over) / (no.of items sold) ) *100.

Let no.of items left over left over be X.

(X) / (20-X) = 0.25

On solving, no.of items sold= (20-X) =16.

Sameer said: (Aug 22, 2012)  
@Sanjeet nice explanation.

Johnny said: (Aug 25, 2012)  
How we came to an assumption that cost of cost of each article = "RS 1" and cost of X articles is rs "X"

Vinay Sharma said: (Sep 4, 2012)  
Let the cost price of one article=Rs 100
profit=25%
SP =100+25=125
NOW
CP of 20 article =SP of X article
20 * 100 = 125 * X
X =16

Meena said: (Sep 22, 2012)  
20*c.p=y --->1
s.p*x=y --->2
Cost price of 20 articles is 100%
Then selling price of x articles is 125%
20*100=2000 --->1
125*x=2000 --->2
x=(2000/125)=16
.'. x=16

Mr K said: (Oct 23, 2012)  
One simple rule in this type of question.

When there is profit 25% it taken as 1.25

So. Equ will be : 20/x=1.25.

X=20/1.25.

X=16.

Ashima said: (Dec 10, 2012)  
Let CP of 1 article be 100rs.
p = 25 (because P% = P/CP*100).
SP = 100 +25 = Rs 125 ( P=SP-CP).

No of articles : CP (unitary method)
1 article - Rs 100.
20 articles - Rs 2000.

No. of articles: SP (unitary method)
1 article - Rs 125
x articles - Rs 2000 (remember CP of 20 = SP of x articles)
x= 2000/125 = 16 articles.

Bhaskar Gairola said: (Dec 14, 2012)  
Let C.P. of 1 article =1.
C.P. of x articles = x.
S.P. of x articles = 1.25x.

Given S.P. of x articales = C.P. of 20 articles.
1.25x = 20.
x=16.

Sri Ram Kumar said: (Jan 4, 2013)  
I got the answer but I am not sure the solution is correct any suggestions please:

C.P of 20 articles=125% of S.P of X articles.

20=125/100 S.P of X articles(here we have to assume C.P of one article to be 1 rupee).

20*100/125=16.

Manish said: (Jan 21, 2013)  
Given C.P of 20 articles = S.P of X articles,

If we consider C.P of 1 article is Rs.1 the S.P of X = 20. from this S.P of 1 articles will be 20/X.

So (20/X - 1)/1*100 =25 which give 16 as a Answer .

Sumit said: (Feb 10, 2013)  
Let, C.P of 20 articles = S.P of x articles = y.

So, C.P of 1 article = y/20.

And, S.P of 1 article = y/x.

((y/x-y/20)/(y/20))*100 = 25 ;

[formula: ((S.P-C.P)/C.P)*100 = gain % ].

(20y-xy)/xy = 25/100

(20/x)-1 = 25/100

20/x = 125/100

x = 16.

Sonu said: (Mar 21, 2013)  
Its very simple to find out the value of x.

The cost price of 20 articles = the selling price of x articles. Here profit is 25% So,

20 = x*(125/100).

2000/125 = x.

So x = 16.

Suku Driver said: (Jul 17, 2013)  
1 step answer:

(1/(20-x)) *100 = 25%.

Simplify, and gets x=16.

Note: (1/(20-x)) is the fraction in terms of Articles.

Kailash said: (Aug 17, 2013)  
Let 1 article price is p.

Then 20 article price will be 20p.

x article price will be = xp.

As per question ...selling price of x articles = sp = 20p.

Cost price of x articles = cp = xp.

=> Gain g = sp - cp= 20p-xp = (20-x)p.

%of gain = {((20-x)p) *100}/xp.

But given Gain = 25%.
=> {((20-x)p) *100}/xp =25.
=> {((20-x)p) *100} =25*xp.
=> {(20-x) *100} = 25*x.

=> {(20-x) *} = (25*x)/100 = x/4.
=> 20 = (x/4.)+x = (5/4)x.

=>x=16.

So here the value of x is 16.

Youth said: (Sep 3, 2013)  
Hey @Kailash I know that you know the answer, but if we do that much lengthy it will take more time. Think about shortcut yaar please. Thank you for giving explanation.

Avi said: (Oct 5, 2013)  
simplest method:

Here give 25% profit means 125/100 ok means 5/4 ratio so 20 article.

1st type 4/5*20=16.

2nd type 5/4 do multiply by 4 both because be need 20 article so get 16 sp.

Chandan Kumar said: (Nov 24, 2013)  
We can also use formula this type of question.

If the cost price of M article is equal to selling price N article
then.

%gain/loss = (M-N/N)*100.
If M>N it is gain% if M<N it loss%.

Solution:- 25 = (20-X/x)*100.
25x = 2000-100x.

125x = 2000.
x = 2000/125.

x = 16.

Shailusha said: (Dec 23, 2013)  
I am not able to understand this problem, can anyone explain this.

Sruthi said: (Dec 25, 2013)  
Please explain this problem with step by step procedure.

Riya said: (Jan 13, 2014)  
Solution:

Suppose,
CP=4.
SP=5.

Given in the question that,
CP of 20 Articles=SP of x Article.

Now put the value,
20*4 = x*5.
80 = x*5.
80/5 = x.
16 = x.

Aqeel said: (Jan 30, 2014)  
No I don't understand the logic for the solution.

Nilesh said: (Jan 31, 2014)  
How 20-x, can you explain that?

Sadee said: (Feb 13, 2014)  
C.P*20 = S.P*x.
x = C.P*20/S.P.

Gain% = gain/C.P = S.P-C.P/C.P = S.P/C.P-1.

25% = 1/4 = S.P/C.P-1.
C.P/S.P = 4/5.

x = 20*4/5 = 16.

Naveen said: (Feb 14, 2014)  
C.P of 20 articles = S.P of x articles.

C.P*20 = S.P*x -->eqn 1.

We know that S.P = [(100+gain%)/100]*C.P.

Gain% is given as 25.

Substituting this in eqn 1 we get x = 16.

Subrar said: (Feb 23, 2014)  
Lets cost price of each article be 4.
So cost price of 20 articles = 20*4=80.
So selling price of each article = 4+4*25%= 5.

So selling price of x articles = 5x.
So according to the question 5x = 80.
So x = 80/5= 16.

Kalyanam said: (Feb 27, 2014)  
Simple it is.

S.P for x articles = C.P (of 20 articles).
Then S.P for 20 articles = ?

S.P = (20/x) *C.P---------- 1.

Profit%= (profit/C.P) *100.
(25/100)*C.P = profit, so profit=C.P/4----------- 2.

But actually formula.
S.P - C.P = profit.

From 1 & 2.

(20/x) *C.P - C.P = C.P/4.

20/x = 5/4.

X= (20/5) *4=16.

I think you understand this simple way of thinking.

Just logic:

In question : profit% has given so S.P>C.P.

So if S.P for xnos is equal to C.P for 20nos.

So S.P for 20nos should be more than S.P for x nos then we will get profit.

So simply S.P for 20 nos > S.P for x nos.

We know already S.P for x nos = C.P.

Then you can find S.P for 20 nos.

That's it.

Taniya said: (Mar 29, 2014)  
I wanted to ask why do we take the C.P of x articles? in the Question it is stated that the C.P of 20 articles so we should find the C.P of 20 instead, no?

Noah said: (Mar 29, 2014)  
Ok lets assume.

Cost price be x and.
Selling price be y.

Since:
(S.P - C.P) / S.P *100 = profit.

Then,

(y - x)/y * 100 = 25/100.
(y - x)/y = 1/4.

When you cross multiply.

4(y - x) = y.
4y - 4x = y.
5y = 4x.

From the question S.P = C.P.

5y = 4*20.
5y/5 = 80/5.

y = 16.

Johir said: (Apr 15, 2014)  
Let 20 article price = 20 RS.

.'. Selling price of x article = 20.
25% profit(means cost is 100 then sp 125).

If SP 125 then CP 100.
...... 20 ..... (100/125)*20 = 16.

Himanshu said: (May 20, 2014)  
SP = 20.
Gain = 25%.
CP = ?

CP = (100*20)/(100+25).

Pavan Divi said: (May 29, 2014)  
Let cost price of an article be "a"
Let selling price of an article be "b"

Cost price of 20 articles is the same as the selling price of x articles. i.e;
20*a = x*b.

Profit = 25%.
((total articles * b) - (total articles * a))/(total articles * a) = 25 /100.

=> (20b-20a)/20a = 1/4.
=> b=5a/4.

Substitute b in 1st equation,
x=16.

Geek said: (Jun 15, 2014)  
It is very simple.

It is given CP of some number of articles is equal to the SP of other number of articles.

Something like this,

CP of 20 apples = SP of 15 apples.

20*CP of each apple= 15*SP of each apple.

20*CP = 15*SP.

NOW just put the formula.
Gain% = CP-SP/CP*100.

Raju said: (Jun 22, 2014)  
Can you explain me about the assumptions it makes me difficult to understand?

Abhinav Sharma said: (Jun 30, 2014)  
Now, This is simplest way I could relate:

No. of articles = 20.
Let CP of 1 article = Re. 1.
CP of 20 articles = Rs. 20 ..... (Eq. 1).

SP of 1 article = 1.25x1 = Rs. 1.25 (Since profit is 25%).
SP of X articles = 1.25X .... (Eq. 2).

Now, the statement says the CP of 20 articles = SP of "X" articles with a profit of 25% i.e. Eq. 1 = Eq. 2.

20 = 1.25X.
X= 20/1.25 = 16.

Hope it clears !.

Chinmaya said: (Aug 15, 2014)  
Let SP of 1 article = RS 1.
Then SP of X articles = RS X.

ACCORDING TO GIVEN,
CP of 20 articles = SP of X articles.
CP of 20 articles = RS X.
CP of 1 article = RS X/20.

SP = CP ( 1 + R/100 ).
1 = 125/100 * X/20.
X = 16. ans (this is the most simplest way).

Joy Ghosh said: (Sep 8, 2014)  
Let cost price of total =100.

Now cost price of one = 100/20=4.
Now sell price of one = 4*125/100=5.

Now we know c.p of 20 = s.p of X .
Then 20*4 = 5*X.

Or x= 16 answer.

Pritam said: (Sep 16, 2014)  
How 100/20=4? @Joy ghosh.

Sasha said: (Sep 27, 2014)  
Let CP for 20 articles be y then one article price = y/20.
SP for x articles is also y, then one article SP = x/y.

Now, since profit is 25%:

Profit on 1 article(out of 20)+CP of one article = SP of 1 article(out of x).
(y/20)*(125/100)=(y/x).
Therefore, x=16.

Abhimanyu said: (Oct 4, 2014)  
20 article C.P = 100rs(say).

Note: When given profit percentage, he calculates it only after selling all goods.

So 20 articles S.P = 125 (SINCE PROFIT PERCENT =25%).
Now consider only S.P.

125 rs --->20 articles.
100 rs --->? articles.
100*20/125 = 16.

That is it simple.

Ashwin said: (Oct 18, 2014)  
Let us consider cost price of 20 articles = 20CP.
And selling price of x articles = xSP.

As he said SP of x articles is same as CP of 20 articles we take,
20CP = xSP.
SP = (20CP)/x.

Profit(.25) = SP-CP/CP.

(20CP-xCP)/xCP = .25.
i.e (20-x)/x = .25.

Implies x = 16.

Santosh Dalal said: (Oct 25, 2014)  
Hello friends.

We can use given below method or not ?

125/100*x = 20.

=> x = 20*100/125.

=> x = 16.

Micmysty said: (Nov 17, 2014)  
The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is:

1. Number of unsold articles = 20-x.

2. In proportion to number of sold articles (x) = 20-x/x.

Number of sold articles is equal to 1 article in 4 = 1/4.

20-x/x = 0.25.

0.25x = 20-x.

0.25x+x = 20.

1.25x = 20.

20/1.25 = 16.

Subhrajyoti Roy said: (Nov 20, 2014)  
PROFIT = 25%.

SO, FOR 1 ARTICLES. IF C.P = 100 THEN, S.P = 125.

∴ 20*C.P = X*S.P[C.P OF 20 ARTICLES = S.P OF X ARTICLES].

=> 20*100 = X*125.

=> X = (20*100)/125.

=> 16 ANS.

Shrinidhi said: (Dec 16, 2014)  
Superb explanation to all. Thank you.

Ravi said: (Dec 26, 2014)  
Hello everyone.

In the given problem 20 article C.P = X.

If one article price is one rupee then X = 20.

Md. Ahasanul Kabir said: (Jan 1, 2015)  
x+x*25/100 = 20.
x+x/4 = 20.
5x = 80.
x = 16.

Samjith P V said: (Jan 2, 2015)  
x*CP*125/100 = CP*20.

Then x = (20*100)/125.

x =16.

Sampath said: (Feb 16, 2015)  
We have 20*C.P = X*S.P and we have profit of 25% which means (S.P-C.P)/C.P = 25/100 = 1/4.

= 4*S.P = 5*C.P => C.P = 4/5 S.P substitute it in first line 20*4/5 S.P = X*S.P =>16.

S.P = X*C.P => X = 16.

Sharang Raina said: (Feb 18, 2015)  
Let cost of one article be Rs 1.

i.e 4 CP = Rs 1.

Now CP of 20 articles is equal to SP of x article.

SP*x = 20*1.

SP = 20/x.

We know,

SP = (1+ P/100)*CP.

20/x = (1+(25/100))*1.

x = RS.16 Answer.

Tarate Shyam Prabhakar said: (Mar 6, 2015)  
I say,

20 articles are same price of CP and SP then 25% profit is there.

That's why 20+(25% profit).

Azu said: (Mar 19, 2015)  
Ok, cool see this guys:

As it was given 20(C.P) = x(S.P)--(1).

And {[(S.P)-(C.P)]/C.P} = 0.25--(2).

Solving, x = 16.

Niru said: (Apr 10, 2015)  
If the profit % = 25 %.

Then S.P= 125... C.P.
Let this be equation 1.

And it is given that 20 article's cost price is equal to x article's selling price, by converting to equation we get,
20*C.P = x*S.P.

By substituting the first equation in S.P we get,
(20*100)/125.
= 16.

Vibin Joy said: (Apr 19, 2015)  
Let CP = a; SP = b;

Then 20a = bx;

Given profit % = 25;

So, b-a/a = 1/4;

Then 5a = 4b;

Compare this with 20a = bx;

Ans = x = 16;

Reepen Dhital said: (Apr 21, 2015)  
Let C.P. of each article be Re. 1 C.P. of x articles = Rs. x.

S.P. of x articles = Rs. 20.

Profit = Rs. (20-x).

Then,

25% of x = 20-x.
25x/100 = 20-x.

25x = 2000-100x.
125x = 2000.

i.e x = 15.

Ravi said: (May 11, 2015)  
Please help me to solve this equation.

(20 - x)/x*100 = 25.
2000 - 100 x = 25 x.
125 x = 2000.

How we get 25x in first step?

Sulekhareddy said: (May 18, 2015)  
C.P = 20.
S.P = X.

Here C.P of 20 articles is same as S.P of X articles.

So, we can assume that, 20 = X.

So, X = 1/20.

S.P = [(100+profit%)/100]C.P.

X = [(100+25)/100]1/20.

= 125/100*1/20.
= 5/4*1/20 = 5/80.
= 1/16.

So X = 16.

Jaya Darshini said: (May 28, 2015)  
Please explain me how come we assume that the CP of 1 article is Rs. 1. Why can't we assume some other value?

Govin said: (Jun 19, 2015)  
Profit = SP-CP.

CP of 20 articles = SP of x articles.

Thus, SP = 20, here assume cost price for this as y.

Profit = 25%.

So, 0.25y = SP-y.
= 0.25y = 20-y.
y = 16.

S.P.Bharath said: (Jun 20, 2015)  
1. Assume any value for cost price.

Let it be Rs.20 (you can assume any value).

Then, according to question, He bought 20 articles each costs Rs. 20.

So 20*20=400.

2. He sells each article at 25% profit. So 25% of C.P Rs. 20 is Rs. 5.

So he sells each article at Rs. 25.25*x = 400. So x = 16.

Gayathri Ganesan said: (Jun 20, 2015)  
@Jaya Darshini.

By default if no such values provided for computation in sense we assume such small value as possible that so we assume 1 here.

Gaurav Sharma said: (Jun 21, 2015)  
C.P. of 20 articles = S.P of x articles = Let Rs 100 (I will write a for article).

Then if C.P. of 20a = Rs 100 (I have taken above).

So C.P. of 1 a = 100/20 = Rs 5.

Now we can take C.P. of x a = Rs 5x.

And S.P of x a = Rs 100 (taken in 1st line).

Now if we have C.P. and SP of X a, so take profit.

i.e (100-5x/5x)100 = 25.

So after solving this you will get x=16.

As I have taken 100 you can take y, 1, or any other variable just we need to equate.

Prudhvi said: (Aug 2, 2015)  
Sp contains cp and profit[25%].

=>x+x/4[25% of x] = 20.

x+x/4 = 20.
=> 5x/4 = 20.

5x = 80.
x = 16.

Shivanandam said: (Aug 4, 2015)  
Answer is 15 coming.

If we go with options. A) 15.

Profit% = (25-15)/20*100 = 25% profit.

Then answer is 15 right.

Sumanth Geras said: (Aug 13, 2015)  
Another method if you do not understand or remember any method.

It may help you. Take cost of 20 articles price 100.

20*5 = 100.

Profit is 25% (i.e 25 rupees).

20*y = 125.

y = 6.25.

So each article price is 6. 25.

Given cost of 20 1 articles is equal to S.P of x articles x*6.25 = 100.

x = 100/6.25 = 16.

Raviteja said: (Aug 15, 2015)  
Given that 20 C.P = x S.P.
And S.P/C.P = 1.25.

20/x = 1.25.
x = 20/1.25.
x = 16.

Kumar said: (Aug 17, 2015)  
I can't understand about xy please explain.

Shameer said: (Aug 20, 2015)  
Use the formula:

CP = (SP*100)/(100+profit).

CP = (20*100)/(100+25).

CP = 16.

Bharath said: (Aug 23, 2015)  
C.P of each article be R.S 1. So 20 article is 20 R.S.

We need to find S.P of x = R.S 20. Profit is 25%.

So 25% of 20 is 5 R.S.
= 25/100*20 = 5.

So S.P is 20+5 = 25.
= 25/20 = 1.25 for 1 article.
= 1.25*16 = 20.

So it is 16.

Guru said: (Aug 27, 2015)  
Nice question.

Jimmy said: (Sep 9, 2015)  
Supposed that the price of 20 articles is 100$.

Then the selling price is 100$ + 100$*0.25 = 125$.

Since the cost price is equal to the to sold price of x article.

We get 20 articles can be sold for 125$.

x articles can be sold for 100$.

x = 100$*20/125$.

x = 16 articles.

Mano said: (Sep 14, 2015)  
Hi guys I can't understand this line:

S.P. of x articles = Rs. 20.

Deep said: (Sep 22, 2015)  
I think it should be 25 if C.P is 200 of 20 articles.

Sathya said: (Sep 24, 2015)  
Profit on one article = (20/x)-1.

% profit = ((20/x)-1)*100)/1 = 25 how this step is used?

Ninteen You Dip said: (Sep 25, 2015)  
Today I know maths is a tricky game which can be played through own idea.

Mahnoor said: (Sep 29, 2015)  
We have to know about value of x? So there is 20 Articles and profit is 25 so put the formula.

SP = (100+gain /100*CP).

Thus (100+25/100*25).

So now calculate it 125/20000.

16 answer.

If I'm wrong then correct me ?

Soumya said: (Oct 3, 2015)  
C.P of 20 = S.P of x.

20 C.P = S.P x.

C.P/S.P = x/20.

i.e. C.P = x and S.P = 20.

Gain = S.P-C.P.

= 20-x.

So gain% = (gain/C.P)*100.

= (20-x)/x*100 = 25 (given).

= (2000-100x)/x = 25.

2000 = 125x-100x = 2000 = 25x.

x = 2000/25 = 16.

We can calculate this type of question through this method check.

Scott said: (Oct 22, 2015)  
The question is not that it is too hard to understand, it is that the question makes no sense in plain English. If you are trying to get someone to figure out what the cost of an article is that costs 20 Rs or $ or any other denomination with a 25% profit, then perhaps you should actually ask that question.

Rajwardhan said: (Nov 12, 2015)  
Let C.P of 1 article Re. 1.

Than C.P of 20 articles is Rs. 20.

Therefore S.P of x articles is Rs. 20.

S.P of x article is Rs. 20.

S.P of 1 article is Rs. (20/x).

Profit on 1 article is = SP-CP.

= (20/x)-1.

Profit = 25% = ((20/x)-1)*100.

25x = (20-x)*100.

x = 16 answer.

Lourdhurani said: (Nov 14, 2015)  
I could not understood please help me.

Poritosh Modak said: (Nov 25, 2015)  
Let costing price = 100 Rs;

Profit = 25%.

Then selling price = (100+25) = 125 Rs.

If selling prices 125 then costing price 100 Rs.

If selling price 1 then costing price 100 Rs = (100/125) = 4/5.

If selling price 20 then costing price 100 Rs = (4/5)*20 = 16.

Answer: 16.

A.Venugopal said: (Dec 5, 2015)  
Let us problem given profit percentage 25%.

Cost price of articles = 1 rupee.

Then 20 article cost = 20*1 = 20 rupees.

Selling price = x (says).

Now profit% = (profit *100)/cp.

Profit = cp-sp.

So (20-x), profit% = 25%.

(25*20)/100 = 20-x.

Then x =15 rupees. Why we don't use this method ?

Subham said: (Dec 11, 2015)  
25% = 1/4.

Out of 5 articles 4 articles sold and 1 is profit.

What about 20 (4 times of 5)?

5 = 4+1.
4 times so, 20 = 16+4.

Shristi said: (Dec 23, 2015)  
Thanks friends for explaining more clearly.

Sriram Praksh said: (Dec 26, 2015)  
Shortcut method:

20 C.P = X S.P.

C.P/S.P = X/20.

Profit 25% --> 125.

So that 125---> 25 means.

100---> ?

Answer = 16.

Shahnewaz said: (Jan 8, 2016)  
100*20 = 125*x.

x = 100*20/125.
x = 16.

Rahul said: (Feb 5, 2016)  
This question is quite simple but the language or the way of asking made in inconvenient to solve. Here is another way to ask the same question.

Cost of an article is 1/20. If you sell it at 25% profit then find out the Selling price?

Abdullah said: (Apr 23, 2016)  
It's VERY EASY!

Let C.P of 1 article is 1Rs. than C.P of 20 articles is 20 RS.

Again S.P of X articles is 20 RS.
So, S.P of 1 article is 20/x.

Now putting the CP and SP of 1 article and profit% in the standard formula given below.

SP = CP*(100 + GAIN)/100.

We have,
20/x =1*(100 + 25)/100.
20/x = 125/100
2000 = 125x.
x = 16.

Subhajit Mitra said: (May 7, 2016)  
Cost price of m article is equal to selling price of n article then,

Gain or loss% = (m - n/n) *100.

Here,

25 = (20 - x/x)/100.

X = 16.

Raunak said: (May 12, 2016)  
@Sanjeet Kumar.

Very well explained and thanks a lot.

Rajender Kumar said: (Jun 6, 2016)  
@Sanjeet could you tell me.

Hence, S. P of x article is Rs. 20.

So S. P. of 1 article = 20/x.

After that, I can't understand why are you using -1 for profit on one article.
Profit on one article= (20/x) - 1.

Please explain me.

Manash said: (Jun 10, 2016)  
Let's assume that the CP of each item is Re 1.

Thus, for 20 items, total CP would be Rs 20.

Given that, he makes a profit of 25%,

ie) He is selling every Re 1 item for Rs. 1.25.

Now, since the CP of 20 items (i.e Rs 20) is equal to the SP of x items, therefore,

x * 1.25 = 20.

=> x= 16.

Pawar Upendra Dinesh Reddy said: (Jul 4, 2016)  
@All

Sanjeet Kumar's explanation is clear and understandable.

Snist said: (Jul 7, 2016)  
It should be noted that only x items are to be considered among 20 items during problem-solving.

So, sp of x items = 20 (since given sp of x = cp og 20 ||consider each item is of rs. 1).

And, cp of x items = x (since he bought the x for rs. X. Likewise 20 items for rs. 20).

Profit for selling x items = sp of x - cp of x = 20 - x.

Profit% = (profit/cp) * 100.

= {(20-x)/x} * 100.

Susanta Halder said: (Jul 18, 2016)  
Thank you sanjeet kumar.

Nat said: (Aug 7, 2016)  
Profit = 25%.
So let c.p = 4 & s.p = 5.
20 * 4 = x * 5 (unknown=x),
16 = x.

Prabhleen Singh said: (Aug 11, 2016)  
Why in this question it is preassumed that C. P of one article is Re.1 and why not Rs.2 or any other value because when we take it to be Rs. 2 it gives x = 32?

Vaishu said: (Aug 19, 2016)  
Why we assume C.P = 100?

Ayush said: (Aug 20, 2016)  
@Prabhleen.

Let assume cp of 1 item is a, and sp of one item is b. Then according to question first line.
20a = xb.

Also by profit statement.

sp = (100 + gain%) cp.

=> b=125%a.

A replacing value of b in the previous equation.

=> 20a = x(125%a).
=> x = (20 * 100) /125.
=> x = 16.

Ranjith said: (Aug 20, 2016)  
How you assume Rs. 100? Please clarify.

M.M Zaman said: (Aug 27, 2016)  
Let the value be X.

Now, 25% of X + X = 20.
i,e X = 16.

Anu said: (Aug 27, 2016)  
Where in this question is given the Dp of one article is re1?

Eesan said: (Sep 2, 2016)  
Let the cost price of 1 article = P.
So C.P. of 20 article = 20P.

Now, S.P. of x articles = C.P. of 20 article.
So, S.P. of 1 article = 20P / x.

Profit = S.P - C.P. = 20P/x - P.

Now profit% = ((S.P. - C.P.) * 100)/C.P.
= ((20P / x) - P) * 100/ P = 16.

Mallesh said: (Sep 5, 2016)  
@Umesh explanation is simple and easily understandable.

Suprotim Paul said: (Sep 9, 2016)  
Good explanation @Sanjeet.

Sreedhar said: (Sep 14, 2016)  
See it's simple.

C.P of 20 article = S.P of X article --> (1)
Let me assume CP of 1 article is 1.
then CP for 20 article it'll be 20.

From condition (1)
CP of 20 article= SP of X article = 20.
Then SP of 1 article = 20/X.

We know that,
Profit %= (SP - CP) * 100/CP.
25 = ((20/X) - 1) * 100).
1/4 = 20 - x/x.
x = 80 - 4X.
5X = 80.
So, x = 16.

Neha said: (Sep 17, 2016)  
See,

CP of 1 article = 1 Rs,
Similarly CP of 20 articles = 20rs.
SP of x articles = 20 rs.
But 25x profit get on 20 Rs.
So,
125x = 20.
100x = ?

(100 * 20)/125 = 16.

So x = 16.

Kishan said: (Sep 22, 2016)  
@Neha. Your explaination superb.

Sairam said: (Sep 22, 2016)  
Friends it is easy.

20 articles are bought.

Then cost price = 20(A)...i.e A is price of each article so cp = 20A.

And given that X articles are sold at B price, then selling price of X articles are = XB.
And given 20A = XB.
Given 25% profit.
So profit% = profit/cp * 100.

Given total profit so, consider 20 articles.
25 = (20B - 20A)/20A * 100;
100A = 80B
So, A/B = 4/5.
4B = 5A.

Given, 20A = XB.
4 * 5A = XB,
4 * 4B = XB,
16B = XB,
X =16.

Netra said: (Oct 2, 2016)  
What do you mean by Profit is 20% of sales (ie 25% of cost)?

Kumar Prabhat said: (Nov 18, 2016)  
(Goods left/Goods sold) 100 => (20 - X/X) * 100 = 25.

Rocky said: (Nov 22, 2016)  
I can't understand this method. So please solve this by another method.

Nithin said: (Dec 2, 2016)  
Guys, I will tell you a basic logic which I felt.

Assumption but it works

25% of profit.

Means
It can be
Sp - Cp = Profit.
125 - 100 = 25.

So no of items which can be bought is 100/125 = 8.

So, the answer must be a multiple of 8.

Sagar said: (Dec 16, 2016)  
Consider CP=100, we know profit 125.
If in 125 rupees - 20 article.
Then in 100 - ?

= 100/125 x 20 = 16.

Nidhi said: (Jan 3, 2017)  
CP. : SP
100% : 125%
4 : 5

Article 5 : 4 (Inversely proportional).
20 : 16

Answer is 16 article.

Kaviarasan said: (Jan 7, 2017)  
@Nithi.

Your explain is very nice easy to understand.

Bhavana said: (Jan 9, 2017)  
Hello, I am confused why profit 25% of cost=20% of the selling price? Explain it.

Ujwal said: (Feb 1, 2017)  
Total SP = sp of x item +sp of 20-x items=cp+sp of 20-x items.
Profit = total sp - total c p =cp + sp of 20-x items-cp = sp of 20-x items.
Profit % = profit * 100/cp.
i.e. 25=(20-x) * 100/x.
Therefore, x =16.

Pooja said: (Feb 5, 2017)  
Your explanation is awesome @Chetan.

David Samuel said: (Feb 15, 2017)  
Given

CP of 20 articles = s.p of x articles --> 1.
From formula (s.p=100+p%/100 x c.p).
We get s.p =5/4 c.p --> 2.
Put 2 in 1.
CP of 20 articles = 5/4 c.p of x articles.
CP of 1 article =(5/4 *1/20) c.p of x articles.

Hence we get x = 16.

Samrat Ghosh said: (Mar 11, 2017)  
Let Cost price of each is a & selling price of each is b.
So, 20 * a = b * X.... i.e 20a = bx -------> (i)
Again, as the profit is 25% so,
a * 125/100 = b...... i.e, 5a = 4b -------> (ii)

Dividing Equation (i) by (ii),
20a/5a = bx/4b.
or, 4 = x/4.
or, x = 16. (ans)

Jbpatel said: (Mar 15, 2017)  
(c.p-s.p)/s.p * 100 = per
(20-x)/x * 100 = 25.

Solve it and you get x=16.

Ajay Choudhary said: (Apr 11, 2017)  
Hello everyone,

We can solve as normal way. Such as
Let,
c.p. of 1 article is = y rupees.
S.p. of 1 article is = z rupees.

So c.p. of 20 articles is= 20y rupees,
c.p of x articles is=xy rupees,
s.p. of x articles is= xz rupees,

Given:
c.p of 20 articles=s.p. of x article
20y = xz

So now we apply the % formula (25 % profit is given).

%profit=(profit /c.p. )x 100.
25=[(s.p. of x articles-c.p of x articles)/c.p. of x articles] X 100,
25=[(xz- xy) / xy] X 100 (put xz=20y),
25=[(20y-xy / xy)] X100 = [(20-x)y / xy ] X100=[20-x/x] X 100,
x =16 (Answer).

Zia said: (Apr 17, 2017)  
Thanks @Ajay Choudhary.

Santanu said: (May 2, 2017)  
This can be done in a simple way:

Say CP is 100, thus SP is 125 (as 25% gain).
According to the condition,
20X100 = 125X x
or, x = 2000/125 = 16 (Ans: b).

Vinuta said: (May 12, 2017)  
Take 20 * c.p = y = > c.p = y/20;
And x * s.p = y = >s.p = y/x;
w.k.t profit% = (100*profit)/c.p;
profit = ((profit%) * c.p)/100;
profit = (25 * c.p)/100;
also profit = s.p - c.p.

(25 * c.p)/100 = (y/x) - (y/20);
= (20 * c.p)/x-c.p;

Take c.p as common
(25 * c.p)/100 = c.p((20/x)-1)
c.p get cancelled
Now,
25/100 = (20/x)-1;
1/4 = (20/x)-1;
(1/4)+1 = 20/x;
5/4 = 20/x;
x = 20*4/5
x = 80/5;
x = 16.

Sm Jahid said: (May 13, 2017)  
Let,
The cp of each article is 1 tk.
The cp of 20 article is = 20 tk.

By the quetion,
The selling price of X article is 20tk.
The cp of 1 article is = 20/X.

The cp of 1 article = 20/x * 100/125.
= 16/X.

Now, 16/X = 1.
So, X = 16.

Lingaraj said: (May 24, 2017)  
Thank you all for the given explanation.

Chintu Jareda said: (May 26, 2017)  
Let, the cost price of one article is = C.P.
Then cost price of 20 article is = 20 * C.P.
And cost price of x article will be =x * C.P.

Given that % profit is 25%.i.e.,prifit = 25% of C.P.

Now we know that, selling price=cost price+profit = 1.25 * C.P.
Hence, selling price of x articles = x * (1.25 * C.P).
Given that s.p. of x article =c.p. of 20article.
x * (1.25 * C.P.) = 20 * C.P.
x = 20/1.25 = 16 Ans.

Suman Sourav said: (Jun 15, 2017)  
If I bought 20 article and sell 16 article that means 4 article saved, gain 25% (125=20 equ i and 100= x.....Equ 2 ) req article 16 will get easily.

Usha said: (Jul 1, 2017)  
Ans: d.
By using the formula.
Sp=(100+gain%)*cp/100.
Here cp of 20 articles = sp of x articles.
So,
Cp of 1 article = sp of x/20 articles.
X/20=(100+25)*1/100,
=>x=25.

Vff said: (Jul 2, 2017)  
why we assume cp =1?

Can anybody explain it?

Saurav Kumar said: (Jul 4, 2017)  
The cost price-100,
selling price-120.
100 * 20 = 125 * x.
After solving value of x=16.

Aravind said: (Jul 5, 2017)  
Can't understand. Please explain me.

Suresh said: (Jul 12, 2017)  
Let C.P. of each article be Re. 2 C.P. of x articles = Rs. x.
S.P. of x articles = Rs. 20.
Profit = Rs. (20 - x).
40 - x x 100 = 25.
x
4000 - 100x = 25x,
125x = 4000,
x = 32.
x cannot be equal to 16.

If you presume Rs.1/- as cost price , x becomes 16. If you presume Rs.10/- as cost price, x becomes 160.

Raja said: (Jul 21, 2017)  
Assume C.p of 20 articles = rs 20 (ie c.p of 1 articles = rs1).

S.p of x articles = c.p of 20 articles,
S.p of x articles = rs 20.
Then c.p of x articles =?.
They told 25% profit.
Profit % =((s.p - c.p)/c.p)*100.
25 = ((20-c.p)/c.p)*100.
C.p of x articles is rs 16.
So, x articles = 16 because c.p of 1 article = rs 1.

Vaishnavi said: (Jul 24, 2017)  
Why this (y-x)=(2x-x) is done? Explain.

Milan Aryal said: (Aug 2, 2017)  
Bina Chand bought two kettles for Rs 1,625. She sold one of them at 20% profit and the others at 20% loss. If the selling price of both kettles are same, find the total cost price of each kettles and find her gain or loss percent in total transaction.

Can anyone solve this?

Darakhshan Anjum said: (Aug 3, 2017)  
Well done @Sanjeet.

Kavya said: (Aug 7, 2017)  
Guys, here the key point is that cost price is same as selling price.

Gyanajyoti said: (Aug 11, 2017)  
Hello @Dosto

Let me explain,
In this sum we take Easy method:
Cp=(100/100+GAIN%)s.p.
so
x=(100/125)20
x=16.

Suman said: (Aug 14, 2017)  
If no of articles are 66 and profit is 22 then what will be the profit %?

Sai Reddy said: (Aug 15, 2017)  
As per given question.

CP of 20 articles =SP of x articles.
CP/SP=X/20.
here CP=x, SP=20.
GAIN%=(GAIN/CP) 100.
25 =(20-X/X)100.
X=16.

Akash Kalyankar said: (Aug 21, 2017)  
Suppose cost of 1 article is 1 rupees.

The cost of 20 articles is 20 rupees.

1) sp of 20 articles will be 25 (with 25 % profit)
2) what will x be for sp = 20; (as cp 0f 20 = sp )

20 -----> 25.
x ------> 20.

x = 20 * 20 / 25.
x = 16.

Kishore said: (Aug 30, 2017)  
Here ,we dont know the value of s.p but in condition given that , s.p of x articles = 20 articles of c.p.

let c.p of 1 article is 1/-
so,c.p of x article become x/-
as per condition,
s.p of x article is 20/-(s.p of x articles which is equal to c.p of 20 article (i.e 20/-)).
p%=(s.p-c.p)/c.p *100.
=(20-x)/x*100 = 16.

Divya Pahwa said: (Sep 12, 2017)  
@Sanjeet Kumar.

Very nice and clear explanation. Thank you.

Basil said: (Sep 17, 2017)  
@Rinku.

Best explanation Really simple. Thank you very much.

Mallesh Goud said: (Sep 22, 2017)  
(a-b) /b*100=gain percentage.

a=20 b=x gain %=25.

If we solve we get x=16.

Purusottam said: (Oct 5, 2017)  
As far as my calculation is concerned it is 18.75.

Utsav said: (Nov 1, 2017)  
@Sanjeet.

"profit on one article= (20/x)-'1'
% profit=((20/x)-'1')*100)/1=25"
Why do we have to subtract 1 in the above two steps?

Vibhore said: (Nov 4, 2017)  
@Utsav.

Profit = SP - CP.
Therefore Profit = (20/x) - 1.
And Profit % = (Profit/CP)X100.

Therefore Profit % = (((20/x)-1)/1)X100 = 25 %.
Ans x = 16.

Jyothsna said: (Nov 7, 2017)  
@Sowmya your explanation is apt without confusing I just wanna to elaborate some of the formulas.

Jyothsna said: (Nov 7, 2017)  
CP 20 = SP x.
CP/SP=x/20.
=>CP =x; SP =20.

Profit=20-x (Profit=SP-CP).
25 = ((20-x)/x)*100 (P%=P/CP*100).

Mamatha said: (Nov 7, 2017)  
Nice explanation guys especially @Jyotsna your formula really works out.

Bharath said: (Nov 19, 2017)  
Just follow the below simple steps.

We assumed that CP of each article is Rs.1 so our SP
Selling Price 20
Profit Percentage 25%
cost Price ?

Well, we all know that SP is inclusive of Profit 25 Percent.Hence in order to calculate the profit, we should calculate as follows 25*125/25 = 4.
Now just deduct your profit from SP.
Which brings up = 16.

Shilpa said: (Nov 21, 2017)  
How did we get profit % as 25%? Please explain.

Aayush Jain said: (Dec 5, 2017)  
We can solve this problem by options.
20 cp= x sp.
cp/sp = x/20.
In the question it is given that profit is 25%.
If we take x=16 we can get out the answer.

Prabhu said: (Dec 6, 2017)  
Say c.p of 20 articles =Rs.100.
S.P of 20 articles = Rs.125 (Because Profit is 25%),
S.P of 1 article = 125/20,
Now S.P of X articles =(125/20)*x =125x/20,
now S.P of X articles = C.P of 20 Articles,
125x/20 = 100,
x= (100*20)/125,
Then value of X =16.

That's it.

Vivek said: (Dec 7, 2017)  
Assume C.P of 1 item = Re. 1.
Therefore, S.P of 1 item = 1.25 (Profit 25%)
For 20 items, C.P = S.P .
20 items * Re. 1 = Rs. 20. <== S.P and C.P (No of items * C.P of 1 item)
x items * Re. 1.25 = Rs. 20 <== This is to find No of items that can be sold for Rs. 20
Usual calculation, find x, bring 1.25 to R.H.S
x = 20/1.25 = 16 items.

Ankit said: (Dec 19, 2017)  
CP*20 = SP* X.
CP/SP=X/20.
%P=(P/CP)*100.
25=(20-X/X)*100.
X=16.

Shakilmehedy said: (Jan 1, 2018)  
We know, profit or loss rate=100/sell price (cost price-cell price),
25=100/x (20-x),
X=16.

Somnath Ghosh said: (Jan 5, 2018)  
Great Explanation @Sanjeet Kumar. Thanks A Lot.

Azad said: (Jan 10, 2018)  
SP/CP=20/x.
25%=1/4 so SP/CP=5/4.
Equating both x= 16.

Rohan said: (Jan 12, 2018)  
Thanks @Chetan.

Jay said: (Jan 23, 2018)  
Bekar explanation, thanks @Sanjeet.

Rajeshwar Emmadoju said: (Jan 28, 2018)  
cp*20=sp*x-----> (1).
profit = 25%.
so,
cp=1y ,sp=1.25y.
from eq 1;

1y*20=x*1.5y.
solve x=20/1.5=16.

Subhanandhini said: (Jan 31, 2018)  
Hi guys,

Here , Given that S.p = 20x.
Profit = 25%.
We need to find the value of x, which is C.P
Hence, C.P=20x÷125*100
125=20x*100
125=2000x
X = 2000÷125
=16.

Rahul Rajshekhar said: (Feb 1, 2018)  
X.SP=20CP.
SP/CP=20/x.
SUPPOSE;
SP=20.
CP=x.
profit=SP-CP=y=20-x.
profit%=y x 100/CP.
25=y x 100/x.
solve it.
then, we get the value of x.

Muddasir Nawaz said: (Feb 16, 2018)  
Lets C.P. of 20 articles=100 rupees.
then S.P. of 20 articles = 125 (with 25% profit).
S.P. of 1 article =125/20 = 6.25.

The C.P. and S.P. is equal which is 100. So one can sale 16 articles having the price of 6.25 in 100 rupees.

As following
100/6.25=16.

Pranay Katkar said: (Feb 24, 2018)  
I got it. Thanks @Chetan.

Gopinath said: (Mar 9, 2018)  
Thanks for explaining @Chetan.

Vatsalya said: (Mar 15, 2018)  
Why it's not 25 can anyone explain?

Sahil said: (Mar 24, 2018)  
@Vatsalya.

If C.P of 20 articles = S.P of 25 articles.

Then there will be a loss, not profit.

Lawrencia said: (Apr 12, 2018)  
I have not understand this. Please explain in detail.

Captain said: (Apr 25, 2018)  
Simple alternative.

x * 125/100 = 20,
125x = 2000,
125x/125 =2000/125,
x = 16.

Sravani said: (Jun 20, 2018)  
CP * 20 articles = SP * x --> (1).
By formula, SP = (100 + profit %) * CP.
=> 125/100 * CP.
substitute in (1),
CP * 20 = 125/100 * CP * x.
x = 2000/125.
x = 16.

Ali said: (Jun 24, 2018)  
The question says the purchase price of 20 articles is the same as the selling price of x.
Let's say that 20 articles cost me 100. This means selling price of x to be 100.
We are unaware of the purchase price of x. But the profit is given i.e. 25%.
Now given the options, when I tried the last option (D = 25). I got profit to be 25%.

Swati Pandey said: (Jun 27, 2018)  
Let the CP of 1 article = 100.
By formula, SP = (100 + profit %) * CP.
125/100 * 100 = 125.
CP of 20 articles = 2000.
CP of 20 articles= SP of x articles.
2000= 125 *x.
Therefore, X = 16.

Anonymous said: (Jun 27, 2018)  
Hi guys, let me try it in a simpler way.

Let C.P of an article be 'y'.
Hence C.P of 20 articles ==> 20y.

But given that 20y = S.P of x articles.
and C.P of x articles is y*x.

Now the profit percentage is:
((S.P of x articles - C.P of x articles)) / C.P of x articles) * 100.

(20y - xy)/(xy) * 100 = 25 (as given profit is 25%)

y cancels out, so we simplify to get x = 16.

Akki said: (Jul 1, 2018)  
Good explanation Thanks @Chetan.

Imran said: (Jul 1, 2018)  
As per my calculation, the solution is;

Let the cost of 20 articles is y Rs then the sp of x articles is y Rs.

cp of 1 article =y/20.
sp of 1 article = y/x.
so profit= (y/x)-(y/20).
so [{(y/x)-(y/20)}/y]*100=25,
by sovling the value oy x =3.8095.

Libia said: (Jul 7, 2018)  
Thanks for making an easy solution @Pinaki Chatterjee.

Chandra Mouli said: (Jul 30, 2018)  
Why we have to assume and take Rs 1 here?

Rohit said: (Aug 16, 2018)  
Why we have to assume and take Rs 1 here?

Can you explain in detail? please.

Ravi Prakash said: (Aug 21, 2018)  
We have a direct formula. that can help to get the answer.

The selling price = (c.p * 100)/ (profit%) + 100
= (20*100)/ (25 + 100).
= 20*100 /(125) = 20*4/5.
= 4*4.
= 16.

Rushikesh said: (Aug 21, 2018)  
We can solve these problem by using another method.

Given 20 C.P.=x S.P --> eq1.
but the profit is 25%.

Therefore, SP=(125/100)*CP.
put above value of SP in eqn 1.
20*CP=x*(125/100)CP.
By solving x=16.

Jyotiranjans Senapati said: (Aug 23, 2018)  
Profit=(20-x).

How it is Possible ?
Profit Means;
For Example One Item Bay 2 Rupees, This Item sell 4 Rupees.
Then Profit 2 Rupees.
Profit How To Calculated.
= Sp-Cp.

Nayana said: (Aug 30, 2018)  
(20-x/x* 100) explain this step clearly.

Radhakrishnan N said: (Sep 10, 2018)  
Cost = Rs 100 For 20=Rs2000,
Sale price of x articles= Rs 2000,
Profit 25% sale price Rs125,
125x = Rs 2000,
X= 2000/125= 16.

Francis said: (Sep 21, 2018)  
It is given that;

20(C.P)=x(S.P).
And we know that,
Profit=(SP-CP) /CP.
Therefore,0.25=(SP-(SP*x/20))/(SP*x/20)).
Solving the equation we have,
x=16.

Jeet said: (Sep 21, 2018)  
Best solution. Thanks @Radhakrishnan.

Shreeshail Karajol said: (Sep 25, 2018)  
(20) cp=(x) sp ------> 1.

Profit=25%.

Means
sp = 125% of cp.
sp = 125/100*((x*sp)/20) {because 1}.
1= 125*x/100*20.
2000/125 = x.
X = 16.

Mounika said: (Nov 20, 2018)  
@Chetan.

Your explanation is good and easy to understand.

Ganesh said: (Dec 4, 2018)  
Profit 25% = 125#
125 - 20
100 - ?.
100 * 20/125 = 16.

Jagadeesh said: (Dec 8, 2018)  
If 20 article=100rs then each article=100/20=5.
X article= 100rs then each article=100/X,
Formula- %profit={(SP-CP)/CP}*100.
25={(100/X-5)/5}*100,
25={(100-5X/X)/5}*100,
25={(100-5X)/5X}*100,
25/100={(100-5X)/5X},
(1/4) 5X=(100-5X),
5X = 400-20X,
5X+20X = 400,
25X = 400,
X = 400/25=16.

Anjali said: (Dec 20, 2018)  
If we have given profit amount and also given a loss amount then how can we calculate the cost price of the product?

Please, anyone, clear my doubt.

Anitya said: (Dec 22, 2018)  
1.25x = 20,
x = 16.

Aisheeka said: (Dec 23, 2018)  
Thanks for your answer @Habib.

Ravi Teja said: (Dec 29, 2018)  
Thanks for the explanation @Sanjeeth.

S.N.V.Subbarao said: (Jan 26, 2019)  
Profit = 25%.

%profit= ((sp-cp) /cp)) * 100.
cp = x.
sp = 20.
25 = (20-x / x)*100.
x = 20 * 4-4x.
3x = 80.
x = 16.

Satyam said: (Feb 5, 2019)  
25 is the answer.

Cost price 20(1+25%100).
20*125%100 = 25.

Mateen Wani said: (Feb 7, 2019)  
CP*20 = SP*X.
CP/SP = X/20.
100/125 = X/20(profit is 25%, therefore if we take CP as 100% then SP will b 125%).
X = 16.

Lily said: (Feb 13, 2019)  
Given:

CP of 20 articles= SP of X articles.
(they said ''Let CP be 1 foe each article'').
For better understanding let be do it with the next number.

Let the CP be 2.

CP fox X articles = 2X.

CP of 20 articles= SP of X articles(given).
2 x 20 = SP for X articles.

Profit= SP - CP.
= 40-2X.

Profit %= Profit x 100/CP.
25 = 40-2X x 100/2X
25 = 20-X x 100/X
X = 20-X x 100/25
X = (20-X) x 4.
X = 80- 4X.
X + 4X = 80.
5X = 80,
X= 16.

Hazard said: (Feb 13, 2019)  
Well said, Thanks @Mateen Wani.

Khan said: (Feb 18, 2019)  
Simple method:

Equation is C. P of 20 articles = SP * x.
C. P is always supposed Rs 100,
P=S.P-CP.
25=S.P-100,
S.P=25+100,
S.P=125.

Now
CP=100,
SP=125,
P=25.

Put into equation
C. P * 20 = sp * x,
100 * 20 = 125 * X,
100 * 20/125 = X.
16 = X.

Anurag said: (Mar 3, 2019)  
I think answer is incorrect because it said the CP of 20 articles = SP.

S.P = x.

Then CP will be of 20 article = 20x.

Ameer said: (Mar 16, 2019)  
Let's say the cost price of 20 articles = 100
the selling price of X articles= 100
Gain=25%.

So the cost price of 1 article = 100/20=5.
The selling price of 1 article = 100/X,
Formula= {100/(100+gain%)} * S.P.
5 = {100/(100+25)} *100/X.
Hence X = 16.

Meheli said: (Mar 17, 2019)  
20 * 100/125 = 16.

Prasad Bhalerao said: (Mar 22, 2019)  
Thanks for solving it @Chetan.

Niveditha said: (Mar 26, 2019)  
It Helped a lot. Thank you @Roopa.

Milan Viradia said: (Apr 17, 2019)  
Let, CP of 1 article = 1 Rs.
Now, Profit = 25%,
SP of 1 article = 1.25.
Hence, SP of x article = x*1.25.

CP of 20 article = SP of x article.
20 = x * 1.25.
x = 20/1.25.
x = 16.

Anomie said: (Apr 17, 2019)  
Nice explanation @Milan.

Vishal said: (Apr 19, 2019)  
Nice explanation @Sanjeet.

Amit said: (May 20, 2019)  
Simply, the solution is;

Take C.P as 100% always.
Now,
100%=x.
Profit is 25% so 100+25.
125%=20,
Solve for x,
Ans is 16.

Rahul Kumar said: (Jun 26, 2019)  
Since profit=25%, SP=125% of CP ---> 1.
CPx20=SPx(X), the subtitute value of CP in 1, we get;
X=16.

Harish said: (Jul 5, 2019)  
20*c.p = x*s.p
Here s.p is 125% of c.p,since there is a profit of 25%.
125% = 5/4,

Therefore,
20*c.p=5/4 (c.p)*x.
c.p get cancelled.
X=16.

Ruturaj said: (Jul 18, 2019)  
Hi.

20 article cp =sp of x article.
( Cp of 1 article =100 , suppose.

Then cp of 20 article =20*100 = which is equivalent to sp of x article.
So,
X article sp = 2000.
X article cp = 100*x.

(25/100) = (2000-100x)/(100x).
X = 16.

Kanchan Das said: (Sep 5, 2019)  
Cost p = selling p = 20.
Let cp=100.
Sp=125.
125 -------------> 100
1 -------------> 100/125
20 -------------> 100/125 * 20.
So, X = 16.

Abhisek said: (Oct 12, 2019)  
Given CP*20 = S.P*x.

And S.P = (100 + gain%)/ 100 *C.P.

Solve the above 2 eqn to get the answer.

Karu said: (Nov 13, 2019)  
Let us assume,

Cost price of 20 articles(cp) = 20 R/s.
Selling price of x articles(sp) = x R/s.

Formula:
(S.P-C.P)/C.P*100=profit;
20-x/x*100 = 25.

Mahesh Bruclee said: (Nov 28, 2019)  
Hi guys,

20 article C.P = 100rs(say)

Note: When given profit percentage, he calculates it only after selling all goods.

So 20 articles S.P = 125 (SINCE PROFIT PERCENT =25%)
Now consider only S.P.
125 rs --->20 articles.
100 rs --->? articles.
100*20/125=16.

That is simple.

Aishu said: (Feb 24, 2020)  
Let C.P of 20 articles be 20rs.
Then S.P of x articles =20rs.
P%=25 (given).
C.P= (100/ (100+p%) ) *S.P.
= (100/ (100+25) ) *20.
=16.

Gopi said: (Mar 12, 2020)  
@Chetan and @Sanjeeth your explanations were good.

Mir Adil Hussain said: (Mar 17, 2020)  
Let C.P of 20 articles = X.
Let S.P be X+20.

By profit% formulae,
125=X+20/X mul by 100.
The answer is 16.

Ashu said: (Mar 23, 2020)  
Nice explain @chetan simple & sweat.

Chaitanya Galande said: (Apr 3, 2020)  
Let Cost price be C and Selling price be S.

Therefore we're given;
20C = S * X.
Now we're given 25 % profit percentage therefore.
C= S/125%.
Or
C = (S*100)/125.
We get C= 4S/5.
Now putting this value in equation 1.
We get;
20* 4S/5 = S*X,
On solving S gets canceled out and value of X.
We get
X=16.

Veer M said: (Apr 12, 2020)  
Let the cost price of one article=Rs 100.
profit=25%,
SP =100+25=125,
NOW;
CP of 20 article =SP of X article.
20 * 100 = 125 * X.
X =16.

Mounika said: (Jun 26, 2020)  
Nice explanation. Thank you @Chetan.

Parimala said: (Jul 23, 2020)  
20C=XS
S/c = 20/x = 5/4.
(Given-25%=+1/4profit=1+4/4=5/4).
5-parts20=5*4 =20 ,then x-4parts = 4 * 4 = 16.
Therefore the answer is 16.

Syed Tufail Nabi said: (Aug 25, 2020)  
Let C.P of 20 articles=Rs. 100= S.P of 20 articles.
Gain %= 25%.
Therefore s.p of 20 articles= Rs. 125.
Hence S.P of 1 article = Rs. 125/20.
Thus S.P of x articles = 100 = (125/20) * x.
Which gives x = 2000/125= 16 Answer.

Rajesh said: (Sep 11, 2020)  
Then after 25% gain selling price of 20 articles is 2500
Then the selling price of 1 article is 2500/20 = 125.
So according to the question:

The Selling price of x article is equal to the cost price of 20 article.
Hence 125x = 2000.
X = 2000/125 = 16,
Hence the value of x is 16.

Pratiksha Jena said: (Sep 13, 2020)  
Right, thanks for the answer @Chetan.

Hrithik said: (Sep 14, 2020)  
Here you can also slove in the following way.

Articales left = 20 - x.
Sold articales = x.
The Profit percentage = (articles left / sold articles) X 100.
25 = (( 20-x )/x) X 100.
And x = 16.

Siddhesh Mhatre said: (Sep 15, 2020)  
20*cp = x*sp.
assume cp = 100 and;
sp = profit + cp = 25 + 100 = 125.

Therefore above equation becomes,
20 * 100 = x * 125.
x = 16.

Devi said: (Sep 29, 2020)  
Given:

Profit =25%=125%
CP of 20=SP of x
CP*20=SP*X
CP/SP=X/20
CP=20;
SP=X;
In percentage method,
CP = 100% always assume.
100%=x ------>1.
125%=20 ------>2.
Cross multiply or divide the eqn 1 & 2.
Then you will get, x=16.

Snr said: (Jan 14, 2021)  
@All.

According to me, the solution is;

CP of 20 articles = SP of x articles.
Profit = 25%.
---> SP = 125% * CP = 1.25 * CP.
---> CP*20 = 1.25*CP*x.
---> 20 = 1.25*x.
---> x = 20/1.25 = 16.

Punyavathi said: (Jan 15, 2021)  
From the above question:

20 articles cost price=selling price of x articles so,
20*c.p = s.p*x ----> (1)
s.p=c.p+profit ----> (2).

Given profit=25%=>1/4 on the cost price.
from equation 2.
20*c.p=(c.p+1/4(c.p))x;
20 c.p=5/4 c.p*x,
x = 16,

Phani said: (Jan 21, 2021)  
CP of 20 articles= SP of X atricles -->(1).

Let us assume the cost price of each article is 1 rupee.so total cost price for 20 articles is 20 * 1 = 20 rupees.

And the given profit is 25%. So for each we article will get a 25% profit on the cost price
so we will sell each article at 1.25 rupee.

So, now we need to multiply this 1.25 rupee to equal it to 20 rupees(because of given equation (1)) and the number with which we multiply 1.25 is the answer.

1.25*16 = 20.

So, 16 is the answer.

Hope this is clear.

Raghib said: (Apr 2, 2021)  
Let's do it simple way.

Let's assume CP=x and SP=y
First-line says;

20CP=NSP
Let's substitute CP and SP values and we get,
20x=Ny ----- (i) This is our first equation

The second part of the question says;
Profit%=25%.
and we know that Profit%=[(SP-CP) X 100]/CP.
by substituting values we get,
25=[(y-x) X 100]/x.
upon solving we get,
x=(4/5)y ---(ii) this is our equation 2.

by substituting equation (ii) in equation (i) we get,
Ny=20 X (4/5)y.
N=16 -- Hence 16 is our answer.

Rony said: (Apr 5, 2021)  
Cp sp profit=25%(fraction value=1/4)

x :20 means cp=4unit & profit = 1unit.
Then sp=5 unit.
Now 5 unit=20 then 4 unit = 16,
Therefore X = 16.

Vishal Thakur said: (May 17, 2021)  
S.P of x Articles = C.P of 20 Articles.

[As C.P of each article is taken as Re. 1].

Therefore, C.P of 20 Articles = Rs. 20.
Therefore, S. P of x Articles = Rs. 20.

Sonam Shah said: (May 20, 2021)  
25% = 1 ÷ 5 =
ie,cp = 4
Sp = 5.

1rs = 1article or 20rs sp so
Sp is nt 5.

Now make sp 20,
Sp=5*4,
So cp also 4*4=16,
Now 1article1rs.
Therefore 16articles =16rs.
So no of articles ie x =16.

Vikash said: (May 28, 2021)  
What if we take cp of 20 articles = rs 100,
then sp of x articles become =rs 100,
and let cp of x articles be =rs x,
Then,
(100 - x/x) * 100 = 25,
which gives x = 80.

Dhanushree Shetty said: (May 28, 2021)  
100+25%=125
20. ?.

Cross multiply you will get it as 20*125/100;
= 16.

Ak said: (May 31, 2021)  
First of all, understand that
Let suppose the c.p of 1 article is 1vs
Then the cost of x article is x rd.
And s.p of x article is equal to 20*1
Which is 20,
And it's given 25%profit which means
25=20-x/x *100,
Then x=16.

Somu said: (Jun 1, 2021)  
Cp of 1 article is Rs. 1 so 20 articles cp is Rs. 20.

Given 25%profit that means on 1 article there is 25% profit so profit is 0.25 on one article then sp of one article is cp + profit = Rs 1.25.

Cp 20 = here we want 20 for how many articles it becomes Rs. 20 @ sp is Rs 1.25 for 4 articles it is 5 so that Rs. 20, 16 articles.

Hanisha said: (Jun 16, 2021)  
Awesome and easy solution @Imraz.

Elvina said: (Jun 29, 2021)  
20cp= xsp ---> (1)
Therefore sp= 20cp/x.

profit%= (profit/cp)100= (sp-cp)100
25=( sp-cp)100

Now substitute the value of sp or cp from (1).
25 = (20cp/x - cp)/cp multiplied by 100,
cp will get cancelled and then solve for x to get 16.

Rhushikesh Shirke said: (Jul 11, 2021)  
Good explanation, thanks @Sanjeet Kumar.

Shambhu Singh said: (Aug 6, 2021)  
Cp of 20 articles = sp of x article.
Cp of 1 artical = sp of x/20 article,
25% frofit.
Cp 1 article is = x/20+25%of x/20.
1= 5x/80.
X=16.

Aksh Sharma said: (Sep 1, 2021)  
Cp of 20 articles = SP of x article.

It means cp = x , Sp = 20.
By formula profit % = (sp - cp) 100/cp.
Therefore. Profit % = Profit % ( for comparing),
(20- x)100/x = 25,
By solving x = 16.

Arotorres said: (Sep 4, 2021)  
20 * C.P = x * S.P ---> (1)
S,P = 1C.P + 0.25 * C.P
S.P = 1.25CP ---> (2).

From (1)
20 * C.P = x * 1.25 * C.P.
c.p gets cancelled;
20/1.25 = x.
x = 16.

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