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Speed, Distance, and Relative Arrival Time

XAT 2010 · Quantitative Ability & Data Interpretation · Medium · Quantitative Ability

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Amarendra and Dharmendra are brothers. One day they start at the same time from their home for Tatanagar railway station in their respective cars. Amarendra took 25 minutes to reach the station. After reaching the station Amarendra found that Dharmendra is 2500 m away from the station. The distance of Tatanagar Station from their home is 15 km. Next day Dharmendra decided to start 7 minutes early. If they drive at the speed same as the previous day then Amarendra will reach the station

  1. A.

    120 seconds earlier than Dharmendra

  2. B.

    120 seconds later than Dharmendra

  3. C.

    300 seconds earlier than Dharmendra

  4. D.

    300 seconds later than Dharmendra

  5. E.

    at the same time with Dharmendra

Answer

B

Explanation

Total distance = 15 km15\text{ km}. Amarendra's time = 25 min   ⟹  \implies Speed = 15/25=0.6 km/min15 / 25 = 0.6\text{ km/min}. Dharmendra covers 15−2.5=12.5 km15 - 2.5 = 12.5\text{ km} in 25 min   ⟹  \implies Speed = 12.5/25=0.5 km/min12.5 / 25 = 0.5\text{ km/min}. Time taken by Dharmendra to reach station = 15/0.5=30 minutes15 / 0.5 = 30\text{ minutes}. On the second day, Dharmendra starts 7 min early. Dharmendra arrives at t=30−7=23 minutest = 30 - 7 = 23\text{ minutes} relative to Amarendra's start time. Amarendra arrives at t=25 minutest = 25\text{ minutes}. Amarendra arrives 25−23=2 minutes=120 seconds25 - 23 = 2\text{ minutes} = 120\text{ seconds} later than Dharmendra.

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