The average weight of 10 oarsmen in a boat is increased by 1.5 kg when one of the crew who weighs 58 kg is replaced by a new man.
Question:

The average weight of 10 oarsmen in a boat is increased by 1.5 kg when one of the crew who weighs 58 kg is replaced by a new man. Find the weight of the new man.

Solution:

Let the average weight of 10 oarsmen be x kg.
Sum of the weights of 10 oarsmen = 10x kg
∴ New average weight = (x + 1.5) kg
Now, we have:

New average weight $=\frac{\text { Sum of the weights of initial } 10 \text { oarsmen- } 58+\text { Weight of the new man }}{10}$

$\Rightarrow x+1.5=\frac{10 x-58+\text { Weight of the new } \operatorname{man}}{10}$

$\Rightarrow$ Weight of the new man $+10 x-58=10 x+15$

$\Rightarrow$ Weight of the new $\operatorname{man}-58=15$

$\Rightarrow$ Weight of the new man $=15+58$

$=73 \mathrm{~kg}$