Aptitude - Profit and Loss - Discussion

Your explanation is awesome @Chetan.

Given

CP of 20 articles = s.p of x articles --> 1.
From formula (s.p=100+p%/100 x c.p).
We get s.p =5/4 c.p --> 2.
Put 2 in 1.
CP of 20 articles = 5/4 c.p of x articles.
CP of 1 article =(5/4 *1/20) c.p of x articles.

Hence we get x = 16.

Let Cost price of each is a & selling price of each is b.
So, 20 * a = b * X.... i.e 20a = bx -------> (i)
Again, as the profit is 25% so,
a * 125/100 = b...... i.e, 5a = 4b -------> (ii)

Dividing Equation (i) by (ii),
20a/5a = bx/4b.
or, 4 = x/4.
or, x = 16. (ans)

(c.p-s.p)/s.p * 100 = per
(20-x)/x * 100 = 25.

Solve it and you get 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).

Thanks @Ajay Choudhary.

This can be done in a simple way:

Say CP is 100, thus SP is 125 (as 25% gain).
According to the condition,
20X100 = 125X x
or, x = 2000/125 = 16 (Ans: b).

Take 20 * c.p = y = > c.p = y/20;
And x * s.p = y = >s.p = y/x;
w.k.t profit% = (100*profit)/c.p;
profit = ((profit%) * c.p)/100;
profit = (25 * c.p)/100;
also profit = s.p - c.p.

(25 * c.p)/100 = (y/x) - (y/20);
= (20 * c.p)/x-c.p;

Take c.p as common
(25 * c.p)/100 = c.p((20/x)-1)
c.p get cancelled
Now,
25/100 = (20/x)-1;
1/4 = (20/x)-1;
(1/4)+1 = 20/x;
5/4 = 20/x;
x = 20*4/5
x = 80/5;
x = 16.

Let,
The cp of each article is 1 tk.
The cp of 20 article is = 20 tk.

By the quetion,
The selling price of X article is 20tk.
The cp of 1 article is = 20/X.

The cp of 1 article = 20/x * 100/125.
= 16/X.

Now, 16/X = 1.
So, X = 16.

Thank you all for the given explanation.