Question

$Rs.1,200$ was divided equally among a certain number of children. Had there been $5$ children more, each would have received $Rs.8$ less. Taking the original number of children as $x$, find the original number of children

• A. $17$
• B. $45$
• C. $12$
• D. $25$

Answer 1

Answer: (D)

$25$

As per the given condition, $x\cdot m=1200$

Also, $(x+5)(m-8)=1200$

If number of children are increased by 5, each gets 8 rs less

Thus, $\frac{1200}{x}-\frac{1200}{x+5}=8$

$1200x+1200\times 5-1200x=8(x^2+5x)$
$750=x^2+5x$
$x^2+5x-750=0$
$x^2+30x-25x-750=0$
$(x+30)(x-25)=0$
$x=25,-30$
Thus, there are $25$ children.