The average weight of 6 persons is increased by 2.5 kg when one of them whose weight is 50kg is replaced by a new man. What is the weight of the new man?

The average weight of 6 persons is increased by 2.5 kg when one of them whose weight is 50kg is replaced by a new man. What is the weight of the new man? 

1).35 kg 

2).65 kg 

3).60 kg 

4).50 kg

Let’s suppose the total weight of six persons before joining the new person is
a kg and the average weight is b kg.

As we know that,

Average of given entities = $(\frac{{{\text{Sum of the given entities}}}}{{{\text{Number of the given entities}}}})$

Hence,     $(\frac{a}{6} = b \Rightarrow {\text{a}} = 6{\text{b}}\ \ \ \ \ \ldots \left( 1 \right))$

Suppose the weight of the new person is c kg.

Hence the total weight of the group = a – 50 + c

And the new average = b + 2.5

Therefore, $(\frac{{{\text{a}}-{\text{}}50{\text{}} + {\text{c}}}}{6} = b + 2.5)$

⇒ a – 50 + c = 6b + 15

From equation (1) we know that a = 6b

⇒ 6b – 50 + c = 6b + 15

⇒ c = 65 kg

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