Question
Download Solution PDFTwo cities X and Y are connected by a regular bus service with a bus leaving in either direction every T min. A girl is driving a scooty with a speed of 60 km/h in the direction X to Y and notices that a bus goes past her every 30 minutes in the direction of her motion, and every 10 minutes in the opposite direction. Choose the correct option for the period T of the bus service and the speed (assumed constant) of the buses.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCorrect option is: (4) 15 min, 120 km/h
|
City X |
City Y |
|---|
t1 = 30 min = 1/2 hr
t2 = 10 min = 1/6 hr
VB = speed of bus
Vg = speed of scooty (girl)
d = (VB − Vg) × t1 = (VB + Vg) × t2
⇒ (VB − 60) × 1/2 = (VB + 60) × 1/6
⇒ 3VB − 180 = VB + 60
⇒ 2VB = 240 = 120 km/h
Distance = (VB − VS) × t1
D = (120 − 60) × 1/2 = 30 km
t = d / VB = 30 / 120 = 1/4 hr = 15 min
Last updated on Jun 16, 2025
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