Question : The ratio of the present age of the father to that of his son is 7 : 2. If after 10 years the ratio of their ages becomes 9 : 4, then the present age of the father is:
Option 1: 43 years
Option 2: 35 years
Option 3: 37 years
Option 4: 40 years
Correct Answer: 35 years
Solution :
Let the present age of the father be $7x$ years, and the present age of the son be $2x$ years.
After 10 years, the father's age will be $7x + 10$, and the son's age will be $2x + 10$.
According to the question,
After 10 years, the ratio of their ages will be $9: 4$.
$\therefore$ $\frac{7x + 10}{2x + 10} = \frac{9}{4}$
⇒ $4(7x + 10) = 9(2x + 10)$
⇒ $28x + 40 = 18x + 90$
⇒ $28x - 18x + 40 = 90$
⇒ $10x + 40 = 90$
⇒ $10x = 90 - 40$
⇒ $10x = 50$
⇒ $x = 5$
So, the present age of the father is $7x$ = 7$\times$5 = 35 years.
Hence, the correct answer is 35 years.
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