Question 75

# City Bus Corporation runs two buses from terminus A to terminus B,one from each of the terminuses such that each bus makes 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 )

Solution

Let the distance between two termini = $$P$$ km
Let the speed of the bus started from Terminus A be x and that of the bus started from terminus B be y.
The two buses met at a distance of 7km from Terminus A
Since the time of travel for both buses is the same.
$$\frac{7}{x}$$=$$\frac{P-7}{y}$$
$$\frac{x}{y}$$=$$\frac{7}{P-7}$$     ----------- Eq (1)
They met again at a distance of 4 km from terminus B.
Distance travelled by bus which started from Terminus A = P+4
Distance travelled by bus which started from Terminus A = 2P-4
So $$\frac{x}{y}$$ = $$\frac{P+4}{2P-4}$$   --Eg (2)
On solving Eq 1& 2, we get P=17 km
Each bus covers a distance of 17*2=34 km on a round trip.
Each bus makes 5 round trips in a day =34*5=170 km
Cost of running one bus = $$170 \times 20 = 3400$$
$$\therefore$$ Cost of running both buses = $$3400 \times 2 = Rs. 6,800$$