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Speed, Time and Distance - Quant/Math - CAT 2013
Question 4 the day:
August 22, 2003
The question for the day is from the topic of Speed, Time and Distance.
- 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 |
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(2) |
32 mph |
| (3) |
20 mph |
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(4) |
None of these |
Correct Answer - (3)
Solution:
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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