Question : The sum of the present ages of father and son is 90 years. 10 years earlier, the ratio of their ages was 5 : 2 The present age of the father is:
Option 1: $65$ years
Option 2: $68$ years
Option 3: $60$ years
Option 4: $70$ years
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Correct Answer: $60$ years
Solution : Given: The sum of the present ages of father and son is 90 years. Let the age of the father be $x$ and that of the son be $y$. So, $x + y = 90$ ⇒ $y = 90 - x$ -----------------------------------------(1) 10 years ago, $ ⇒ \frac{x-10}{y-10} = \frac{5}{2}$ ⇒ $2x - 20 = 5y - 50$ ⇒$ 2x + 30 = 5y$ By putting the value of $y$ from (1) ⇒ $2x + 30 = 5×(90 – x)$ ⇒ $2x + 30 = 450 – 5x$ ⇒ $7x = 420$ ⇒ $x = 60$ Hence, the correct answer is $60$ years.
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