Q. If the average of $m$ numbers is $n^{2}$ and $n$ numbers is $m^{2}$ then what will be the average of $( m + n )$ numbers:
Answer:
$mn$
Notes: Because the average of $m$ numbers is $n^{2}$,
and the average of $n$ numbers is $m^{2}$
Since the sum of $m$ numbers is $=m n^{2}$
and the sum of $n$ numbers is $=n m^{2}$
Now we have to find the average of $( m + n )$ numbers :
$\frac{m n^{2}+n m^{2}}{(m+n)}=\frac{m n(n+m)}{(m+n)}=m n$
Hence option [D] is the right answer.