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 = 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.