Question

एक व्यक्ति 100रू अपने मित्रों में बराबर बाँटे । यदि उसके पांच मित्र अधिक होते हैं तो प्रत्येक को एक रू कम मिलता | उनके कितने मित्र थे?

Answer 1

Say there are x friends.

You want to divide 100 rupees into x friends

then each friend will get 100/x.

Now it says if you have 5 more friends then total number of friends will be (x+5)

In that case each friend will get 100/(x+5).

Question says that in the new situation, each friend will get 1 rupee less. so we can write equation:

$\frac{100}{x}-1=\frac{100}{x+5}$

multiply both side by x(x+5) to cancel out denominators.

$\frac{100*x*(x+5)}{x}-1*x*(x+5)=\frac{100*x*(x+5)}{x+5}$

100(x+5)-x(x+5)=100x

$100x+500-x^2-5x=100x$

$500-x^2-5x=0$

$0=x^2+5x-500$

$x^2+5x-500=0$

$x^2-20x+25x-500=0$

x(x-20)+25(x-20)=0

(x-20)(x+25)=0

which gives x=20, x=-25

money can't be negative so we will use x=20

So the final answer is, there are 20 friends.