1.

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»

(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

⇒ \(\bigg(\frac{x}{10}+\frac{x}{15}\bigg)-\)\(\bigg(\frac{x}{12.5}+\frac{x}{12.5}\bigg)\) = \(\frac{12}{60}\)

⇒ \(\bigg(\frac{3x+2x}{30}\bigg)\) - \(\frac{2x}{12.5} = \)\(\frac{12}{60}\)

⇒ \(\frac{x}{6}-\frac{2x}{12.5}= \) \(\frac{12}{60}\) ⇒ \(\frac{12.5x-12x}{75}=\) \(\frac{12}{60}\)

⇒ 0.5x = 75 x \(\frac{12}{60}\) ⇒ \(x\) = \(\frac{75\times12}{0.5\times60}=\) 30 km.


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