Question

The average weight of 5 men is increased by 2 kg when one of the men whose weight is 60 kg is replaced by a new man. The weight of the new man is:
$\left(a\right)50Kg$
$\left(b\right)65Kg$
$\left(c\right)68Kg$
$\left(d\right)70Kg$

Answer 1

Hint: We need to find the weight of the newly added man using the information given about averages. For this question to be done we should be aware about the concept of averages. We will assume the average weight of 5 men to be a variable $x$ and then we will proceed with the information given to produce the result.

Complete step by step answer:
It should be known that the average of $n$ number of quantities is obtained by summing up those $n$ quantities and dividing the sum by $n$. Here $n=5$ and we will take the average to be a variable.
Let us suppose that the average weight of 5 men is $x$. Then according to the definition of average:
$x=\dfrac{\text{Sum of weights of 5 men}}{5}$
$\implies \text{Sum of weights of 5 men}=5x$
Now suppose that the weight of the new man is $N$. Then since the new man has been placed at the place of man whose weight is 60Kg, we get the following:
$\implies \text{Sum of weights of 5 men}=5x-60+N$
Also, the average weight has increased by 2Kg. We can say that the average has now become $x+2$ so we can say that:
$x+2=\dfrac{5x-60+N}{5}$
$\implies 5x+10=5x-60+N$
$\implies N=70Kg$
Hence, the weight of the new man is 70Kg. So, option $\left(d\right)70Kg$ is correct.

Note: We don’t need to really calculate the weight of each person in order to solve this question. We should use the trick as shown here to solve questions like these in the least time possible and the most accurate answer will be produced.