Aptitude - Profit and Loss - Discussion

I am not able to understand this problem, can anyone explain this.

Please explain this problem with step by step procedure.

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.

No I don't understand the logic for the solution.

How 20-x, can you explain that?

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.

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.

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?