Question

If $P$ is the mean of first 21 natural numbers, $Q$ is the mean of the first 24 odd natural numbers and $R$ is the mean of the squares of the first 12 natural numbers. Then, the average of $P, Q$, and $R$ is_____

Answer 1

Mean of first 21 natural numbers $=\frac{21+1}{2}=11$
Mean of first 14 odd natural numbers $=\frac{(24)^2}{24}=24$
Mean of the squares of first 12 natural numbers $=\frac{11 \times 12 \times 23}{11 \times 6}=46$
$\therefore$ Required average $=\frac{11+24+46}{3}=\frac{81}{3}=27$