Aptitude - Profit and Loss - Discussion

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.

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.

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.

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.

20 * 100/125 = 16.

Thanks for solving it @Chetan.

It Helped a lot. Thank you @Roopa.

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.

Nice explanation @Milan.

Nice explanation @Sanjeet.