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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.

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Solution

If you want to increase the average weight of 10 people by by 1.5kg, you are in other words, trying to increase the total weight of the people by 15kg (10 * 1.5 =15).
So, the new guy needs to be 15kg heavier than the 59kg person. That means that the weight of th new guy would be 73kg (58 + 15 = 73).

Solution 2:
Let the average weight of the ten people at the start be x kg.
Let the new guy's weight be y kg.

So, we get:
10x - 58 = 10 (x+1.5) - y
10x - 58 = 10x + 15 - y
-73 = -y
y = 73

Therefore, the new guy's weight is 73kg.

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