If the average of m numbers is n² and that of n numbers is m², then the average of (m+n) numbers is · ABC26GN1577
Subject: General Aptitude · Chapter: Average · Exam: S.S.C. 2008
If the average of $m$ numbers is $n^{2}$ and that of $n$ numbers is $m^{2}$, then the average of $(m+n)$ numbers is
(a)$m-n$
(b)$m n$
(c)$m+n$
(d)$\frac{m}{n}$
Answer
Answer (as printed): B
Explanation
Sum of $m$ numbers $=m n^{2}$. Sum of $n$ numbers $=n m^{2}$. Sum of $(m+n)$ numbers $=m n^{2}+n m^{2}=m n(m+n)$. $$\therefore \quad \text { Average of }(m+n) \text { numbers }=\frac{m n(m+n)}{(m+n)}=m n .$$
Explanation as extracted from the printed page; notation may be imperfect.