Question

The students of a class contributed for a programme. Each student contributed the same amount. Had there been $15$ more students in the class and each student had contributed Rs. $40$ less. The total amount contributed would have increased from Rs. $3000$ to Rs. $3200$. Find the strength of the class.

• A. $20$
• B. $25$
• C. $30$
• D. $35$

Answer 1

Answer: (B)

$25$

Let the number of students be $s$ and contribution of each be $c$
Given,
$s\times c=$ Rs. $3000$ --- $\left(1\right)$
And $(s+15)\times (c-40)=3200$
$=>sc-40s+15c-600=3200$
$=>sc-40s+15c=3800$ --- $\left(2\right)$
From, eqn $\left(1\right)$
$=>3000-40s+15c=3800$
$=>15c=40s+800$
$=>c=\frac{8s+160}{3}$ --- $\left(3\right)$
From eqns $\left(1\right)$ and $\left(3\right)$
$=>s\times \frac{8s+160}{3}=3000$
$=>8s^2+160s=9000$
$=>s^2+20s-1125=0$
Solving it we get $s=25$