Multiple choice

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 ?

  1. $\displaystyle \frac{ra-sb}{r-s}$ years
  2. $\displaystyle \frac{ra+sb}{r-s}$ years
  3. $\displaystyle \frac{ra-sb}{r+s}$ years

  4. None of the above
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A Correct answer
Explanation

Total age of r boys is r * a. Total age of s boys is s * b. The sum of ages of the remaining (r - s) boys is (r * a - s * b). The average age is (r * a - s * b) / (r - s).

AI explanation

The total age of all r boys is ra years, and the total age of the s boys is sb years. Using the basic average formula, the sum of the ages of the remaining boys equals the total age minus the age of the s boys, which is ra - sb. Dividing this remaining sum by the number of remaining boys gives the average age of the remaining boys as (ra - sb) divided by (r - s) years.

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