If the average of s numbers is $r^4$ and the average of r numbers is $s^4$, then find the average of all r + s numbers?
Answer & explanation
Correct answer: option 1
Sum of s numbers = s$r^4$
Sum of r numbers = r$s^4$
Sum of r + s = r$s^4$ + s$r^4$
Average of r + s = \(\frac{r\;s^4\;+\;s\;r^4\;}{r + s}\)
⇒ \(\frac{rs (s³ + r³)}{r + s}\)
⇒ \(\frac{rs(s + r)(s² + r² - sr)}{(r + s)}\)
⇒ (s² + r² - sr)