Aptitude - Profit and Loss - Discussion

Let us assume c.p of one article = rs.1.
c.p of x articles = x,
s.p of x articles = c.p of 20 articles = 20,
profit = s.p-c.p = 20-x.
profit% = 25%.
profit% = (profit/c.p )* 100.
25 = (20-x/x )*100.
25x = 2000-100x.
2000 = 125x.
x=16.

Let Cp of 1 article = y
Then Cp of 20 article = 20y = sp of x article(from cp of 20 articles same as sp of x article)
Now cp of x articles = xy.

Gain = sp of x articles - cp of x articles.
Now profit = gain/cp of x article*100
25=20y-xy/xy * 100.
By solving 5xy/4 = 20y
then 5x =80.
X = 16.

Simply using the formula:

SP = 100 + profit × CP/100.
CP : SP.
X: 20.
Simply putting the value you will get the 16 as answer.

Given:
20cp = x sp.
20cp = 125% cp * x (because profit is 25 %).
20cp = 5/4 cp * x.
20 x 4/5 = x.
16 = cp.

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].

If c.p of an article is 4 and s.p of an article is 5.

c.p of articles is equal to s.p of 16 article;
So,20*4=16*5=80.

s.p of 20 article is 20*5 = 100.
c.p of 20 article is 20*4 = 80.
Profit is 20.
20/80 *100=25%.

CP of 20= SP of x
sp/cp = 20/x.
sp-cp/cp = 20-x/x.
profit percentage = 25%.
Therefore,25/100 = 20-x/x.
Solving we get x = 16.

Deriving formula:

S.P = [100 + gain% / 100 ] x C.P.
S.P is x.
C.P is 20x, so one CP is x/20,
x = 125/100 x (x/20),
x = 125x/2000,
2000x = 125x,
= 16.

Selling Price of X article is 20 and, we have to find C.P. of this X article.
It can be calculated by using the formula of C.P. which is given below;
C.P. = 100/(100+Gain%) * S.P.

So, let C.P. be X.. And by given data Gain % = 25, and S.P. of X article = 20 putting this values we get,

X(c.p) = 100/(100+25) * 20(s.p).
X= (100/125) * 20,
= 0.8 * 20,
= 16.

@Shahil Shaji.

Nice explanation keep rocking. Thanks.