Question : The ratio of the ages of Ram and Shyam 15 years ago was 2 : 5. The ratio of their present ages is 5 : 8. What will be the present age of Shyam (in years)?
Option 1: 10
Option 2: 15
Option 3: 25
Option 4: 40
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Correct Answer: 40
Solution : Given: Ratio of the ages of Ram and Shyam (15 years ago) = 2 : 5 The ratio of ages of Ram and Shyam (present) = 5 : 8 Let the ages of Ram and Shyam be $x$ and $y$ respectively. So, $x : y=5 : 8$ ⇒ $\frac{x}{y}=\frac{5}{8}$ ⇒ $x=\frac{5y}{8}$ --------------------------- (1) 15 years ago, the ratio was 2 : 5 ⇒ $\frac{x-15}{y-15} = \frac{2}{5}$ ⇒ 5$x$ – 75 = 2$y$ – 30 ⇒ 5$x$ – 2$y$ = 75 – 30 ⇒ 5$x$ – 2$y$ = 45 By putting the value of $x$ from (1) ⇒ 5 ×$\frac{5y}{8}$ – 2$y$ = 45 ⇒ 9$y$ = 360 ⇒ $y$ = $\frac{360}{9}$ = 40 Hence, the correct answer is 40 years.
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