Question

A father is six times as old as his son and the mother is five times as old as the son. The sum of
the father's and the mother's age is 77 yrs. What is the age of the father?
(1) 42 yrs
(2) 45 yrs
(3) 36 yrs
(4) 48 yrs
to yrs​

Answer 1

Step-by-step explanation:

Given :-

• Father's age is six times the son's age.
• Mother's age is five times the son's age.
• Sum of father's and mother's age is 77.

To find :-

Age of father

Solution :-

Let the son's age be x.

Then,

father's age = 6x

mother's age = 5x

It is given that,

6x + 5x = 77

There is no more condition.

So, it not possible to get the answer by a proper method.

Therefore, we start guessing.

1. If son's age was 6 years,

• father's age = 6x = 36 years
• mother's age = 5x = 30 years
• Sum of father's and mother's age = 36 + 30 = 66
• But, 66 ≠ 77
• Therefore, son's age cannot be 6 years.

2. If son's age was 7 years,

• father's age = 6x = 42 years
• mother's age = 5x = 35 years
• Sum of father's and mother's age = 42 + 35 = 77
• This time, 77 = 77

Therefore, son's age = 7 years

Father's age = 6x = 42 years

Hope it helps!

Answer 2

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$Given :-$

Father's age is six times the son's age.

Mother's age is five times the son's age.

Sum of father's and mother's age is 77.

$To find :-$

Age of father

$Solution :-$

Let the son's age be x.

Then,

father's age = 6x

mother's age = 5x

It is given that,

6x + 5x = 77

There is no more condition.

So, it not possible to get the answer by a proper method.

Therefore, we start guessing.

If son's age was 6 years,

father's age = 6x = 36 years

mother's age = 5x = 30 years

Sum of father's and mother's age = 36 + 30 = 66

But, 66 ≠ 77

Therefore, son's age cannot be 6 years.

If son's age was 7 years,

father's age = 6x = 42 years

mother's age = 5x = 35 years

Sum of father's and mother's age = 42 + 35 = 77

This time, 77 = 77

Therefore, son's age = 7 years

Father's age = 6x = 42 years

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