Question

Everyday a bus leaves Delhi for Ambala and at same instant bus leaves Ambala for Delhi. The two buses cross each other at Karnal. Yesterday the bus leaving Delhi started late by 30 minutes ,as a result of which it met the bus going in the opposite direction 12 km short of usual meeting point. Today the bus leaving Ambala started late by 30 minutes, as a result of which it made the bus going in the the opposite direction 12 minutes later than their usual meeting point.what is the speed of the bus going from delhi to ambala?

Answer 1

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

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

Solution:

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

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

 

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

Distance from Delhi to karnal = XT  km

Distance from Ambala to karnal = 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 ambala Bus  =  XT - 12  km

Distance covered by Ambala to karnal = YT + 12 km

t is time taken by Bus from  Ambala to meeting point  , hence another bus traveled 30 mins less

XT - 12   =  X(t  - 30/60)

YT + 12  = Yt

=> (X + Y)T  = (X + Y)t - X/2

bus leaving Ambala started late by 30 minutes,

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

Distance Covered by Ambala 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 ambala  = 60  km/hr

Learn More:

Amar and Akbar left Bhubaneshwar simultaneously and travelled ...

https://brainly.in/question/9633837

A and B left kanpur simultaneously and travelled Lucknow.A speed ...

https://brainly.in/question/13051323

Two trains R and S start from rest simultaneously from stations A and ...

https://brainly.in/question/8932282