Question : The speeds of two bodies are in the ratio 2 : 3. If the difference in the time taken to cover 50 m is 10 sec, then find the difference in their speeds.
Option 1: $\frac{8}{9} \mathrm{~m} / \mathrm{sec}$
Option 2: $\frac{5}{6} \mathrm{~m} / \mathrm{sec}$
Option 3: $\frac{6}{5} \mathrm{~m} / \mathrm{sec}$
Option 4: $\frac{7}{5} \mathrm{~m} / \mathrm{sec}$
Correct Answer: $\frac{5}{6} \mathrm{~m} / \mathrm{sec}$
Solution : Let the speed of two bodies be $2x$ and $3x$. Time taken by first body = $\frac{50}{2x}$ Time taken by second body = $\frac{50}{3x}$ According to the question, $\frac{50}{2x}-\frac{50}{3x}=10$ ⇒ $\frac{150-100}{6x}=10$ ⇒ $50=60x$ ⇒ $x=\frac{50}{60}=\frac{5}{6}$ Hence, the correct answer is $\frac{5}{6} \mathrm{~m} / \mathrm{sec}$.
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