Speed Time Distance Questions : Relative speeds, opposite directions : Ascent CAT, XAT, TANCET Courses, study material

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Speed, Time, Distance : CAT 2016 Quant Practice Questions

Question 4 the day : August 22, 2003
The question for the day is from the topic Speed, Time and Distance. The question helps understanding relative speeds and time taken to cover a certain distance while traveling in opposite directions.

Yana and Gupta leave points x and y towards y and x respectively simultaneously and travel in the same route. After meeting each other on the way, Yana takes 4 hours to reach her destination, while Gupta takes 9 hours to reach his destination. If the speed of Yana is 48 km/hr, what is the speed of Gupta?
  1. 72 kmph
  2. 32 mph
  3. 20 mph
  4. None of these
Correct Answer 20 mph. Choice (3) is right.

Explanatory Answer

Yana and Gupta travel for the same amount of time till the time they meet between x and y.
So, the distance covered by them will be the same as the ratio of their speeds.

Let the time that they have taken to meet each other be x hours from the time they have started.
Therefore, the cover the entire distance, Yana would take x + 4 hours and Gupta will take x + 9 hours.

Ratio of time taken Yana : Gupta :: x + 4 :: x + 9
=> Ratio of speeds of Yana : Gupta :: x + 9 :: x + 4 or 1 :

By the time Yana and Gupta meet, Yana would have traveled 48X kms. After meeting, this is the distance that Gupta takes 9 hours to cover.

Hence, Gupta's speed =  km/hr.
But we know that the ratio of Yana's and Gupta's speeds are 1 :

Therefore, 48 :  :: 1 :
Or  =
=> x2 + 9x = 9x + 36

=> x2 = 36 or x = 6 hours.

Hence, speed of Gupta =   = 32 kmph = 20mph

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