XAT 2012 — QA & DI Question 18
Answer the following question based on the information given below.
Ramya, based in Shanpur, took her car for a 400 km trip to Rampur. She maintained a log of the odometer readings and the amount of petrol she purchased at different petrol pumps at different prices (given below). Her car already had 10 litres of petrol at the start of the journey, and she first purchased petrol at the start of the journey, as given in table below, and she had 5 litres remaining at the end of the journey.
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City Bus Corporation runs two buses from terminus A to terminus B, each bus making 5 round trips in a day. There are no stops in between. These buses ply back and forth on the same route at different but uniform speeds. Each morning the buses start at 7 AM from the respective terminuses. They meet for the first time at a distance of 7 km from terminus A. Their next meeting is at a distance of 4 km from terminus B, while travelling in opposite directions. Assuming that the time taken by the buses at the terminuses is negligibly small, and the cost of running a bus is Rs. 20 per km, find the daily cost of running the buses (in Rs.).
Answer & solution
- A
3200
- B
4000
- C
6400
6800
- E
None of the above
Let the distance between the two terminuses be x km.
Now, relative distance travel by the two buses before they meet for the first time = x km
Similarly, relative distance travelled by the two buses after first meet and before second meet = 2x
Now, bus originating from terminus A travels 7 km before the first meet.
Hence, it should travel 2 × 7 = 14 km after first meet and before second meet.
Hence, total distance travelled by that bus before second meet = 7 + 14 = 21 km
Now, second meet occurs at 4 km from the terminus B.
Hence, total distance travelled by the bus starting from terminus A (from the beginning till they meet for the second time) = x + 4 km
Hence, x + 4 = 21
Hence, x = 17 km
Hence, one bus travels 34 × 5 = 170 km a day.
Hence, cost of running one bus = 170 × 20 = Rs. 3400
Hence, cost of running two buses = 3400 × 2 = Rs. 6800
Hence, option (d).