Question

The average age of $r$ boys in a class is $a$ years. If the average age of $s$ of them is $b$ years, then what is the average age of the remaining boys ?

• A. $\frac{ra-sb}{r-s}$ years
• B. $\frac{ra+sb}{r-s}$ years
• C. $\frac{ra-sb}{r+s}$ years
• D. None of the above

Answer 1

Answer: (A)

$\frac{ra-sb}{r-s}$ years

Total age of $r$ boys $=rxa=ra$ years
Total age of $s$ boys $=sxb=sb$ years
Therefore, total age of remaining boys $=ra-sb$
Total number of remaining boys $=r-s$
Therefore, average age of remaining boys $=$ $\frac{ra-sb}{r-s}$ years.