Aptitude - Profit and Loss - Discussion

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.

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

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).

Let's say C.P of one article be "k" and S.P of one article be "y".

So, C.P of 20 article is "20k" and S.P of x article is "xy'

According to the question we know,
C.P of 20 article = S.P of x article.
Therefore, 20k = xy ------------> (1)

Also for a profit of 25% we can write equation as,
=> S.P of one article - C.P of one article / C.P of one article X 100 = 25
=> y - k / k = 1/4
=> 4y = 5k ------------> (2)

From equation (1) and (2) we can say that,
=> 16y - xy = 0,
=> y(16-x) = 0,
=> x = 16 [ANS].

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.

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.

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.

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.

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.

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.