A father is nine times as old as his son and the mother is eight times as old as the son. The sum of the father’s and the mother’s age is 51 years.…

Correct Option (4)

Let the son's age be represented by 'x' years.

According to the problem statement:

• The father's age is nine times the son's age, so Father's age = 9x years.
• The mother's age is eight times the son's age, so Mother's age = 8x years.

The sum of the father's and mother's age is given as 51 years. Therefore, we can set up the equation:

9x + 8x = 51

Combining the terms:

17x = 51

Solving for x:

x = $\frac{51}{17}$1751​

x = 3

Thus, the son's age is 3 years.

Incorrect Options:

Substituting the values from the other options into the problem's conditions demonstrates their inconsistency:

• If the son's age were 7 years (Option 1): Father's age = 9 × 7 = 63 years; Mother's age = 8 × 7 = 56 years. The sum of their ages would be 63 + 56 = 119 years, which does not equal 51.
• If the son's age were 5 years (Option 2): Father's age = 9 × 5 = 45 years; Mother's age = 8 × 5 = 40 years. The sum of their ages would be 45 + 40 = 85 years, which does not equal 51.
• If the son's age were 4 years (Option 3): Father's age = 9 × 4 = 36 years; Mother's age = 8 × 4 = 32 years. The sum of their ages would be 36 + 32 = 68 years, which does not equal 51.