The average age of 5 children of a family is 15 years. Average age of children together with their father and mother is 25 years. If the father is older than the mother by 4 years, then find the age of mother (in years).

Given:

The average age of 5 children = 15 years

Average age of children with their father and mother = 25 years

Age difference between father and mother = 4 years

Formula used:

Average = Sum of values/Number of values

Calculation:

Let the age of the mother be M years.

We know that the average age of the 5 children is 15 years.

Therefore, the sum of the ages of the 5 children is (15 × 5) = 75 years.

Also, the average age of the children together with their father and mother is 25 years.

Since there are 5 children, the total number of people in the family is 5 + 2 (father and mother) = 7.

Using the formula for the average, we can write the equation:

(75 + M + F)/7 = 25

where F represents the age of the father.

We are also given that the father is older than the mother by 4 years:

F = M + 4

Now we can solve the equations.

Substituting F = M + 4 in the first equation:

(75 + M + M + 4)/7 = 25

Simplifying:

(2M + 79)/7 = 25

2M + 79 = 175

2M = 175 - 79

2M = 96

M = 96/2

M = 48

Therefore, the age of the mother is 48 years.