Question

If the mean weight of 8 people is increased by 4 when a person of weight 30 kg is replaced by another man, find the weight of the new man.

Answer:

The weight of the new man is 62 kg.

Let the mean of the 8 people be x kg.
Therefore, the sum of weights = 8x kg.
Let the weight of the new man be y kg.
When a person of weight 30 kg is replaced by the new man, the new sum of weights = (8x-30+y) kg.
Thus, the mean of the newly formed group which consists of 8 members = (8x-30+y)/8 which is given to be equal to x+4.
Therefore, we have the equation:
(8x-30+y)/8 = x+4
⇒ 8x-30+y = 8x+32
⇒ y = 32+30
⇒ y = 62
Therefore, we get the weight of the new man equal to 62 kg.


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