A sum of money is equally divided among a number of children. Had there been 16 children more, each would have received ₹ 2 less and had there been 16 fewer, each would have received ₹ 3 more. Find the sum of the money distributed.
(a)₹ 880
(b)₹ 896
(c)₹ 928
(d)₹ 960
Answer
Answer (as printed): D
Explanation
Let the total number of children be $n$ and the amount received by each child be $₹x$. Then, total sum distributed $=₹(nx)$. So, $(n+16)(x-2)=nx \Leftrightarrow nx-2n+16x-32=nx \Leftrightarrow 16x-2n=32$ ...(i) And, $(n-16)(x+3)=nx \Leftrightarrow nx+3n-16x-48=nx \Leftrightarrow 16x-3n=-48$ ...(ii) Subtracting (ii) from (i), we get: $n=80$. Putting $n=80$ in (i), we get: $16x=192$ or $x=12$. Hence, total sum distributed $=nx=₹(80 \times 12)=₹960$.
Explanation as extracted from the printed page; notation may be imperfect.