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InterviewSolution
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Two town A and B are connected by a regular bus service with a bus leaving in either direction every T minutes. A man leaving in either direction every in the direction A to B notices that a bus goes past him every 18 min in the direction of his motion, and every 6 min in the opposite direction. The period T of the bus service isA. 4.5 minB. 9 minC. 1.2 minD. 24 min |
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Answer» Correct Answer - B Let `v "km"h^(-1)` be the constant speed with which the bus travel ply between the towns A and B. Relative velocity of the bus from A to B with respect to the cyclist = `(v - 20) km h^(-1)` Relative velocity of the bus from B to A with respect to the cyclist `= (v + 20) km h^(-1)` Distance travelled by the bus in time T (minutes) = vT As per question `(vT)/v - 20 = 18` or `vT = 18v - 18 xx 20` and `(vT)/v + 20 = 6` ...(i) or `vT = 6v + 20 xx 6` ....(ii) Equaitons (i) and (ii), we get `18v - 18 xx 20 = 6v + 20 xx 6` or `12 v = 20 xx 6 + 18 xx 20 = 480` or v = `40 km h^(-1)` Putting this value of v in (i) , we get `40T = 18 xx 40 - 18 xx 20 = 18 xx 20` or T = `18 xx 20/40` = 9 min |
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