Question

Q9. The sum of ages of 55 children born at the intervals of 33 years each is 5050 years. Find out the age of the youngest child? A. 66 years B. 55 years C. 44 years D. 33 years

Answer 1

Given:

The sum of ages of 55 children born at the intervals of 33 years each is 5050 years.

To find:

The age of the youngest child

Solution:

We know,

$\boxed{\bold{S_n = \frac{n}{2}[2a + (n-1)d] }}$

where Sₙ = sum of n terms, a = first term, d = common difference and n = no. of terms

The given situation in the question forms an A.P. where,

"n" → no. of children = 5

"a" → the age of the youngest child

"Tₙ" → the age of the eldest child

"d" → the children are born at a regular interval = 3.

"Sₙ" → the sum of ages of 5 children = 5  

Now, by substituting the given values in the formula of Sₙ, we get

$S_n = \frac{n}{2}[2a + (n-1)d]$

$\implies 50 = \frac{5}{2} [2a + (5-1)3]$

$\implies 50 = \frac{5}{2} [2a + (4)3]$

$\implies 50 = \frac{5}{2} [2a + 12]$

$\implies 50 = 5a + 30$

$\implies 5a = 50 - 30$

$\implies 5a = 20$

$\implies \bold{a = 4}$ ← option (c)

Thus, the age of the youngest child is → 4 years.

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