A girl is replaced by a boy and average is increased by 1 $\frac{1}{2}$ kg. If the total number of students was $40$ and their average weight was $30$ , then calculate the weight of the new boy.

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Solution

$\Rightarrow$ The average weight of $40$ students was $30$
$∴$ Sum of weight of $40$ students $= (40 \times 30) k g = 1200 k g$
$\Rightarrow$ When a girl is replaced by boy the average weight becomes $31 \frac{1}{2} k g$ .
$∴$ Sum of weight of $40$ students after replacing girl by boy $= 40 \times 31 \frac{1}{2} = 40 \times \frac{63}{2} = 1260 k g$
$\Rightarrow$ The weight of new boy $= (1260 - 1200) k g = 60 k g$

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A girl is replaced by a boy and average is increased by 112kg. If the total number of students was 40 and their average weight was 30, then calculate the weight of the new boy.

⇒ The average weight of 40 students was 30∴ Sum of weight of 40 students =(40×30)kg=1200kg⇒ When a girl is replaced by boy the average weight becomes 3112kg.∴ Sum of weight of 40 students after replacing girl by boy =40×3112=40×632=1260kg⇒ The weight of new boy =(1260−1200)kg=60kg

A girl is replaced by a boy and average is increased by 1 $\frac{1}{2}$ kg. If the total number of students was $40$ and their average weight was $30$ , then calculate the weight of the new boy.