Aptitude - Profit and Loss - Discussion

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.

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.

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.

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.

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?

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.

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.

SP = 20.
Gain = 25%.
CP = ?

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

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.

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.