# 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 = 10*x* 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 $=15+58$

$=73 \mathrm{~kg}$

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