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What will be the weight of the new man, if the average weight of 10 oarsmen in a boat increases by 1.5 kg when a new man replaces one of the crew who weighs 58 kg?

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75 kg

73 kg

77 kg

71 kg

answer is B.

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Detailed Solution

We have to find the weight of the new man, if the average weight of 10 oarsmen in a boat increases by 1.5 kg when a new man replaces one of the crew who weighs 58 kg.
We know that,

Mean= Sum of all observations Number of observations

Suppose the mean is ‘y’.

Sum of all weights 10 = y Sum of all weights = 10 y

Let the new man’s weight be ‘x’ after replacement.

Sum of all weights − 58 + x 10 = y + 1.5 Sum of all weights − 58 + x = 10 y + 15 Sum of all weights + x = 10 y + 15 + 58 Sum of all weights + x = 10 y + 73

We can observe that sum of all weights are 10y.

10 y + x = 10 y + 73 x = 73

Hence, the weight of the new man is 73kg.
Therefore, option 2 is correct.

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