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.

Answer 1

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:
$$\begin{gathered} \mathrm{New}\mathrm{average}\mathrm{weight}=\frac{\mathrm{Sum}\mathrm{of}\mathrm{the}\mathrm{weights}\mathrm{of}\mathrm{initial}10\mathrm{oarsmen}-58+\mathrm{Weight}\mathrm{of}\mathrm{the}\mathrm{new}\mathrm{man}}{10} \\ \Rightarrow x+1.5=\frac{10x-58+\mathrm{Weight}\mathrm{of}\mathrm{the}\mathrm{new}\mathrm{man}}{10} \end{gathered}$$

$$\begin{gathered} \Rightarrow \mathrm{Weight}\mathrm{of}\mathrm{the}\mathrm{new}\mathrm{man}+10x-58=10x+15 \\ \Rightarrow \mathrm{Weight}\mathrm{of}\mathrm{the}\mathrm{new}\mathrm{man}-58=15 \\ \Rightarrow \mathrm{Weight}\mathrm{of}\mathrm{the}\mathrm{new}\mathrm{man}=15+58 \\ =73\mathrm{kg} \end{gathered}$$