Question

Ram travels from P to Q at 10 km/hr and returns at 15 km/hr Shyam travels from P to Q and returns at 12.5 km/hr If he takes 12 minutes less than Ram then what is the distance between P and Q?

• A. 60 km
• B. 45 km
• C. 36 km
• D. 30 km

Answer 1

The correct option is D 30 km

Let the distance between P and Q be x km Then Total time taken by Ram in the round trip - Total time taken by Shyam in the round trip = 12 min
$\Rightarrow (\frac{x}{10}+\frac{x}{15})-(\frac{x}{12.5}+\frac{x}{12.5})=\frac{12}{60}\Rightarrow \left(\frac{3x+2x}{30}\right)-\frac{2x}{12.5}=\frac{12}{60}$
$\Rightarrow \frac{x}{6}-\frac{2x}{12.5}=\frac{12}{60}\Rightarrow \frac{12.5x-12x}{75}=\frac{12}{60}$
$\Rightarrow 0.5x=75\times \frac{12}{60}\Rightarrow x=\frac{75\times 12}{0.5\times 60}=30km$