Question

Two 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 scooty with a speed of 60 km/h in the direction X to Y 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.

विकल्प

• 9 min, 40 km/h

• 25 min, 100km/h

• 10 min, 90 km/h

• 15 min, 120 km/h

Answer 1

15 min, 120 km/h

Explanation:

Let v_b = velocity of bus

v_g = velocity of girl = 60 km/h

When moving in the same direction, a bus crosses her every

t₁ =30 min = `1/2 h`

When moving in the opposite direction, a bus crosses her every

t₂ = 10 min = `1/6 h`

Since buses are equispaced.

d = `(v_b - v_g) t_1 = (v_b + v_g) t_2`

d = `(v_b - 60) 1/2 = (v_b + 60) 1/6`

3 v_b − 180 = v_b + 60

3 v_b − v_b =  60 + 180

2 v_b =  240

`v_b = 240/2`

v_b = 120 km/h

Distance = (v_b − v_g)t₁

= `(120 - 60)1/2`

= `(60)1/2`

∵ d = 30 km

Time interval between two successive buses,

T = `d/(v_b)`

= `30/120`

= `1/4 h`

= 15 min