Question

A single rail track exists between two stations X and Y. A superfast
train S leaves station X for station Y at 8:00 AM and when it reaches y,
a passenger train P immediately starts from Y and reaches X by 9:30
A.M. The speed of the superfast train S is double that of express train
E, which in turn is double that of the passenger train P. On a
particular day, due to a technical problem, the superfast train starts
at X,30 minutes behind the normal schedule. If s doubles its speed,
what should be the ratio of the new speeds of the passenger train
and the superfast train such that passenger train reaches exactly at
the scheduled time on that day?​

Answer 1

Answer:

1:240

Step-by-step explanation:

first calculate the distance b/w stations in terms of the given speeds . then calcukate the departure time of both trains . now apolying the given conditions of changed speeds , calculate the new speeds using the original distance .

Answer 2

Given :  Super fast S & passenger P  train between stations X & Y , speed and time to reach

To find :  ratio of the new speeds of the passenger train  and the superfast train

Solution:

The speed of the superfast train S is double that of express train

E, which in turn is double that of the passenger train P

Let say Passenger Train P Speed = P  km.Hr

Then Super fast Train S Speed = 2 * E = 2 * (  2* P )  = 4P  km.hr

Let say Distance between X & Y station = D km

8 to 9 : 30 time = 1 hr 30 mins = 3/2 hrs

then D/4P  + D/P   = 3/2

=> D + 4D  = 6P

=> 5D = 6P

=> D = 1.2P  km

superfast train starts  at X 30 minutes behind the normal schedule

=> Total time taken now = 1 hr

Super  fast train now  = 2 * 4P = 8Pkm / hr

Time Taken by Super fast train =  D/8P  hr

Time taken by Passenger train = 1 - D/8P

Speed of Passenger train  = D/(1 - D/8P)

= D/(1 - D/8P)

= 1.2P/( 1 - 1.2P/8P)

= 1.2P * 8 ( 8 - 1.2)

= 9.6P/6.8

= 48P/34

ratio of the new speeds of the passenger train  and the superfast train

48P/34  : 8P

=> 6 : 34

=> 3 : 17

ratio of the new speeds of the passenger train  and the superfast train  = 3 : 17

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