Question

Sum of the ages of 5 children born at the intervals of 3 years each is 50. What is the age of the middle child?

• A. 8
• B. 10
• C. 13
• D. 17

Answer 1

The correct option is B

10

Sum of ages of 5 children = 50
Difference between their ages = 3
As the ages of children are in Arithmetic Progression
We know the sum and the common difference, to find out the age of middle child we need to find the first term (a)
Sum of an AP = $\frac{n}{2}(2a+(n-1\left)d\right)$

$=\frac{5}{2}(2a+(5-1\left)3\right)$
$\Rightarrow 50=\frac{5}{2}(2a+12)$
$\Rightarrow \frac{50\times 2}{5}=2a+12$
$\Rightarrow 20-12=2a$
$\Rightarrow a=4$
$\therefore$ Age of the middle child = 4 + 3 + 3 = 10 years