Question

Everyday ,a bus leaves Delhi for kurukshetra and at the same instant another bus leaves kurukshetra for Delhi ,the bus crosses each other at gurgaon ,yesterday the bus leaving delhi started by 30 minutes late,as a result it met the bus going in opposite direction 12 km short of the usual meeting point. Today, the bus leaving kurukshetra started late by 30 minutes,as a result two buses met 12 minutes late than the usual timing.whqat is the speed of bus going from delhi to kurukshetra ?

40 Kmph

48 kmph

60 kmph

cannot bet determined

Answer 1

Given :  Everyday a bus leaves Delhi for kurukshetra and at same instant bus leaves kurukshetra for Delhi. The two buses cross each other at gurgaon.

To find :  speed of the bus going from delhi to kurukshetra

Solution:

speed of the bus going from delhi to kurukshetra  = X  km/hr

speed of the bus going from kurukshetra to Delhi  =  Y   km/hr

=> Time taken by both bus to reach gurgaon  = T  hr  

Distance from Delhi to gurgaon = XT  km

Distance from kurukshetra to gurgaon = YT   km

Total Distance = XT + YT

bus leaving Delhi started late by 30 minutes

meet 12 km short of usual meeting point.

Distance covered by delhi to kurukshetra Bus  =  XT - 12  km

Distance covered by kurukshetra to Delhi Bus = YT + 12 km

t is time taken by Bus from  kurukshetra to meeting point  , hence another bus ( from Delhi ) traveled 30 mins less

XT - 12   =  X(t  - 30/60)

YT + 12  = Yt

=> (X + Y)T  = (X + Y)t - X/2

bus leaving kurukshetra started late by 30 minutes,

Distance Covered by Delhi Bus = X ( T + 12/60)  = X( T + 1/5)

Distance Covered by kurukshetra Bus = Y(T+ 12/60 - 30/60) = Y(T - 3/10)

XT + X/5 + YT - 3Y/10  = XT + YT  

=>  X/5  = 3Y/10

=> 2X = 3Y

=> X = 1.5Y

(X + Y)T  = (X + Y)t - X/2

using  X = 1.5Y

=> 2.5YT = 2.5Yt -  1.5Y/2

=> T = t -  1.5Y/5

=>  t - T = 1.5/5   hr

=> t - T  =  18  mins

18 mins taken extra by bus

YT + 12  = Yt

=> Y(t - T)  = 12

=> Y (18/60) = 12

=> Y =  40

  X  =  60  

speed of the bus going from delhi to kurukshetra  = 60  km/hr

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