M4maths Previous Puzzles

18 May 2022 Time Distance & Speed

A bus left point P for point Q. 70 minutes later train left P for Q and arrived at Q at the same time as the bus. If the bus and the train left simultaneously from the opposite ends P and Q towards each other, they would have met in 84 minutes after the start. How much time did it take the bus to travel from P to Q?

OPtion

1) 3 hours
2) 2 hours
3) 4 hours
4) 3 hours 45 minutes
5) 2 hours 45 minutes
6) 2 hours 30 minutes
7) 3 hours 30 minutes
8) 2 hours 15 minutes
9) 3 hours 15 minutes
10) None of these

Solution

Let distance from P and Q = d ; Speed of Bus = x ; Speed of Train = y
Let, time taken by bus to travel distance d = t min. and by train = (t-70) min.
Speed = Distance/Time
x = d/t
y = d/(t-70)
When travelling towards each other time taken=84 min.
⇒ Distance covered by bus in 84 min + Distance covered by train in 84 min = Total distance
(d/t)*84 + [d/(t-70)]*84 = d
84/t + 84/(t-70) = 1
t² - 238t + 5880 = 0
(t-28) (t-210) = 0
t=28, 210
The time 't' can not be less than 70 min as train starts 70 minutes after the bus starts and they meet after some time, .'. t = 210 min = 3 hrs 30 min.
Correct Option 7)

Correct Option: 7 Best Solution (1)

Pargat Pal Singh   2 years AGO

If distance is d and time taken (in minutes) by bus to cover distance d is x, then
Speed of bus= d/x
Speed of train = d/(x-70)
When trainscstart from opposite sides simultaneously..
84*(d/x + d/(x-70)) =d
Solving it, we get,
x=210 minutes or 3 hour 30 minutes

Like? Yes (2) | No