Question

Six years ago, the average age of a family of 5 members was 32 years. During this period, a baby is born in the family. Even now, the average age of the family is the same as it was 6 years ago. What is the age of the baby?
(A) 3 years
(B) 2 years
(C) 4 years
(D) 5 years​

Answer 1

Question-

Six years ago, the average age of a family of 5 members was 32 years. During this period, a baby is born in the family. Even now, the average age of the family is the same as it was 6 years ago. What is the age of the baby? x

Option-

(A) 3 years

(B) 2 years

(C) 4 years

(D) 5 years​

Answer-

Average equals the sum of a set of numbers divided by the count which is the number of the values being added. For three numbers namely x, y and z, their average = $\frac{x+y+z}{3}$

The average age of the family 6 years ago = 32

After 6 years, the ages are =

a + 6

b + 6

c + 6

d + 6

e + 6

Let the age of the baby be f.

Then,

$\frac{(a + 6)+(b+6)+(c+6)+(d+6)+(e+6)+(f)}{6} = 32\\\frac{a + 6+b+6+c+6+d+6+e+6+f}{6} = 32\\\frac{a+b+c+d+e+f+36}{6} = 32\\\frac{a+b+c+d+e+f+36}{6} = 32$

But  $\frac{a+b+c+d+e}{5} = 32$  (Given)

Then substituting,

$\frac{a+b+c+d+e+f+36}{6} = \frac{a+b+c+d+e}{5}$

Divide both the sides by their common factors

$\frac{f+36}{6} = \frac{1}{5}\\f+6=\frac{1}{5}\\f = 3$

So the answer is (A) 3 years.

Answer 2

Given:

Total family members = 5

Their averga age = 32

Time = 6 years

To find:

Age of the baby

Solution:

Average age of a family of 5 members 6 year ago = 32 years

Sum of ages of family members = 5 x 32 = 160

Now, since the baby is born, thus -

sum of age of 6 members = 6 x 32 = 192

Sum of age of a family of 5 members at present -

= 160 + 5 X 6

= 160 + 30

= 190

Therefore, age of child -

= 192 - 190

= 2

Answer: The age of baby is (B) 2 years