1. 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 20 per km, find the daily cost of running the buses (in )
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By: anil on 05 May 2019 02.37 am
Let the distance between two terminus = $$x$$ km Thus, relative distance travelled by the buses before they meet for the first time = $$x$$ km Similarly, relative distance travelled after first and second meet = $$2x$$ km Now, bus originating from terminus A travels 7 km before 1st meet => Distance travelled by it after 1st meet and before 2nd meet = $$2 imes 7 = 14$$ km => Total distance travelled before 2nd meet = $$14 + 7 = 21$$ km Also, 2nd meet occurs at 4 km from terminus B Hence total distance travelled by bus from A = $$x + 4 = 21$$ => $$x = 21 - 4 = 17$$ km Each bus take 5 round trips => Total distance travelled by 2 buses = $$17 imes 2 imes 5 = 170$$ km Cost of running one bus = $$170 imes 20 = 3400$$ $$ herefore$$ Cost of running both buses = $$3400 imes 2 = Rs. 6,800$$
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