The present age of a father is twice as that of his son. 10 years ago, the age of father was thrice the age of his son. If the ratio of present age of son’s mother to father is 9 : 8, then find the difference between present age of mother and son (in years)?

The correct answer is 25 years.

Let the present age of the son be S years, and the present age of the father be F years.

Step 1: Set up the equations from the given conditions.

Condition 1: The present age of the father is twice that of his son.

F=2S...\left(1\right)

Condition 2: 10 years ago, the father's age was thrice the son's age.

(F-10)=3(S-10)...\left(2\right)

Step 2: Substitute equation (1) into equation (2).

Replace F with 2S in equation (2):

2S-10=3S-30

Rearranging:

30-10=3S-2S

S=20\text{years}

Step 3: Find the father's present age.

From equation (1):

F=2\times 20=40\text{years}

Verification: 10 years ago, father was 30 and son was 10. Indeed, 30 = 3 × 10. ✓

Step 4: Find the mother's present age using the given ratio.

The ratio of mother's present age to father's present age is 9 : 8.

\frac{M}{F}=\frac{9}{8}

M=\frac{9}{8}\times F=\frac{9}{8}\times 40=45\text{years}

Step 5: Find the difference between the mother's and son's present ages.

\text{Difference}=M-S=45-20=25\text{years}

The difference between the present age of the mother and the son is 25 years.