If the average of s number is r4 and the average of r numbers is s4, then find the average of all r + s numbers?
A. rs(r2 + s2 - rs)
B. rs
C. r2 + s2
D. rs(r2 + s2)
Answer: Option A
Solution(By Examveda Team)
$$\eqalign{ & {\text{Average}} = \frac{{{\text{Sum}}}}{{{\text{Number}}}} \cr & {\text{Sum}} = {r^4} \times s \cr & {\text{Again sum}} = r \times {s^4} \cr & {\text{Average of all }}r{\text{ and }}s{\text{ numbers}} \cr & = \frac{{{r^4} \times s + r \times {s^4}}}{{r + s}} \cr & = \frac{{rs\left( {{r^3} + {s^3}} \right)}}{{r + s}} \cr & = \frac{{rs\left( {r + s} \right)\left( {{r^2} + {s^2} - rs} \right)}}{{r + s}} \cr & = rs\left( {{r^2} + {s^2} - rs} \right) \cr} $$Related Questions on Average
A. 125 km/hr
B. 75 km/hr
C. 135 km/hr
D. 120 km/hr
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