SSC GD 2023 PYQ — Question 54

The correct answer is Option 3 i.e. 34 kg.

Average = sum of the weight/total person

Let, the members in a group be n, and the original average of the group is x

Sum of the weights = nx

If a person weighing 40 kg joins, then the average weight of a group increases by 1 kg

Now, according to the question

⇒ $\frac{nx+40}{n+1} = x+1$...........................1

If the weight of this person had been 28 kg, then the average weight of the group would have decreased by 1 kg

⇒ $\frac{nx+28}{n+1} = x-1$.......................2

Subtract equation (2) from (1)

⇒ $\frac{nx+40}{n+1} -\frac{nx+28}{n+1}$ = 2

⇒ 12 = 2n + 2

⇒ n = 5

Put the value of n in Equation 1

$\frac{5x+40}{5+1} = x+1$

⇒ 5x + 40 = 6x + 6

x = 34

So, the actual average weight of the group = x = 34 kg