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?
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)