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Byju's Answer

Standard XII

Economics

Value Added Method

Two towns A a...

Question

Two towns A and B are connected by aregular bus service with a bus leaving in either direction every Tminutes. A man cycling with a speed of 20 km h^–1in the direction A to B notices that a bus goes past him every 18 minin the direction of his motion, and every 6 min in the oppositedirection. What is the period Tof the bus service and with what speed (assumed constant)do the buses ply on the road?

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Solution

Let V be thespeed of the bus running between towns A and B.
Speed of the cyclist, v= 20 km/h
Relative speed of thebus moving in the direction of the cyclist
= V – v= (V – 20) km/h
The bus went past thecyclist every 18 min i.e., (whenhe moves in the direction of the bus).
Distance covered by thebus = …(i)
Since one bus leavesafter every T minutes, the distance travelled by the bus willbe equal to
Both equations (i) and(ii) are equal.
Relative speed of thebus moving in the opposite direction of the cyclist
= (V + 20) km/h
Time taken by the busto go past the cyclist
From equations (iii)and (iv), we get

Substituting the valueof V in equation (iv), we get

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