Three trains P, Q and R travel 90 km in 1.5 hr, 2 hr and 3 hr respectively. R starts from a station, at a certain time, Q starts from the s… — Answer & Discussion

Three trains P, Q and R travel 90 km in 1.5 hr, 2 hr and 3 hr respectively. R starts from a station, at a certain time, Q starts from the same point 30 minutes later and P starts from the same station 45 minutes later than R. Then P meets Q and R after

A1 hr, 30 min
B45 min, 45 min
C45 min, 1 hr
D1 hr, 45 min

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Discussion 1

CCommunity23 Apr 2019

Let the time taken by R to reach the meeting point be ‘t’

For meeting point of P and Q

For P:

Speed = 90/1.5 = 60 kmph

Time = (t – 3/4)

∴ Distance = 60 × (t - 3/4)

∴ Distance = 60t – 45

For Q:

Speed = 90/2 = 45 kmph

Time = (t - 1/2)

∴ Distance = 45× (t - 1/2) = 45t – 22.5

Equating the distances ,

60t – 45 = 45t – 22.5

∴ 15t = 22.5

∴ t = 1.5

∴ P meets Q after (t - 3/4) = 0.75 hours = 45 minutes

For the meeting point of P and R

For P:

Speed = 90/1.5 = 60 kmph

Time = (t - 3/4)

∴ Distance = 60t – 45

For R:

Speed = 90/3 = 30 kmph

Time = t

∴ Distance = 30t

Equating the distances ,

60t – 45 = 30t

∴ t = 45/30 = 1.5

∴ P meets R after 1.5 – ¾ = 0.75 hrs = 45 min.