Question

The average age of 4 children is 16 years. If their

mother’s and father’s age is taken into account, the

average age increases by 9 years. Find out the father’s

age if mother’s age is 40 years.​

Answer 1

Given :-

• The average age of 4 children is 16 years.
• If their mother’s and father’s age is taken into account, the average age increases by 9 years.
• mother’s age is 40 years.

To Find :-

• Age of Father ?

Solution :-

Given that, The average age of 4 children is 16 years.

So,

→ Average = (sum of ages) / (Total member)

→ sum of ages od all 4 children = Average * 4 = 9 * 4 = 36 years.

Now, mother’s and father’s age is also included , and average increased by 9 years.

So ,

→ Total members now = 4 children + mother + Father = 6

→ New average = 9 + 9 = 18 years.

Therefore,

→ sum of all ages = (New average) * (Total members) = 18 * 6 = 108 years.

Hence,

→ Sum of ages of mother and father = (Sum of all ages) - (sum of ages of 4 children) = 108 - 36 = 72 years.

Now, we have given that, mother age is 40 years.

So,

→ Mother + Father = 72

→ 40 + Father = 72

→ Father = 72 - 40

→ Father = 32 years. (Ans.)

∴ father’s age is 32 years.

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