Question

A sum of $Rs.120$ was distributed among a certain number of boys. If there had been $4$ boys less, each would have received a rupee more. Find the number of boys.

• A. $20$
• B. $24$
• C. $28$
• D. $30$

Answer 1

The correct option is B $24$

Let there be $n$ boys and each gets $p$ rupees.
then, $np=120$

$\therefore p=\frac{120}{n}$
and $(n+4)(p-1)=120$

$(n+4)(\frac{120}{n}-1)=120$

$(n+4)(120-n)=120n$
$120n+480-n^2-4n=120n$
$n^2+4n-480=0$
$n^2+24n-20n-480=0$
$(n+20)(n-24)=0$
$n=-20,24$

$\therefore n=24$