Question

Neeraj is going to Agra on his bike from Delhi. He overtakes a bus traveling from Delhi to Agra at 4.30 pm. Neeraj reaches Agra at 6 pm. After stopping there for an hour, he starts back towards Delhi and meets the same bus at 7.30 pm which was moving towards Agra at that time. If both the bus and the bike were traveling with uniform speeds on the same route, at what time would the bus reach Agra?

Options

• 9.45 pm

• 9.30 pm

• 9.15 pm

• 9 pm

Answer 1

9 pm

Explanation:

Let the bus and bike meet at any point 'C' between Delhi and Agra at the time 4:30 p.m. such that distance of point C from Agra is d km.

Now, Distance Covered by bike d km in 1.5 hours.

So, speed of the bike = `"d"/1.5 = "2d"/3` km/hr

After taking 1-hour rest, biker started its return journey and meet the bus at 7: 30 pm.

So, distance covered by biker in 30 minutes

`= "2d"/3 xx 30/60 = "d"/3` km

Now, distance covered by the bus in time 4:30 pm to 7:30 pm = `"d" - "d"/3 = "2d"/3` km

∴ Speed of the Bus = `("2d"/3)/3 = "2d"/9` km/hr

Now, time is taken by the bus to cover a distance `"d"/3` km

`= ("d"/3)/("2d"/9) = 9/(3 xx 2) = 1.5 "hrs"`

= 1 hors 30 min.

Hence, Bus will reach Agra at 7:30 p.m. + 1 hour 30 min.

= 9: 00 p.m