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
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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