SSC GD 2024 PYQ — Question 47

The correct answer is option 4 i.e. 36 years.

 

( S) be the sum of the ages of the original 22 men.

( A) be the average age of the 22 men initially, 

⇒ $A = \frac{S}{22}$

Their combined age is:

⇒ 58 ×  2 = 116

 The total sum of the ages of the 22 men becomes ( S - 116 + x ).

The average age of the new group is 2 years less than the original average, i.e. ( A - 2 ). 

⇒ $\frac{S - 116 + x}{22} = A - 2$

 

⇒ $\frac{S - 116 + x}{22} = \frac{S}{22} - 2$

⇒ S - 116 + x = S - 44

⇒ x - 116 = -44

⇒ x =  72

The sum of the ages of the two new men is 72.

⇒ $\frac{x}{2} = \frac{72}{2} = 36$

The  average age of the two new men is (36).