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Speed, Time and Distance - Quant/Math - CAT 2013

  1. Algebra
  2. Progressions
  3. Averages
  4. Clocks and Calendars
  5. Data Sufficiency
  6. English Grammar
  7. Function
  8. Geometry
  9. Coordinate Geometry
  10. Interest
  11. Mensuration
  12. Mixtures & Alligations
  13. Number System
  14. Percentages
  15. Permutation & Combination
  16. Pipes & Cisterns And Work & Time
  17. Probability
  18. Profit & Loss
  19. Races
  20. Ratio, Proportion
  21. Speed, Time & Distance
  22. Trigonometry
  23. Miscellaneous
  24. General Knowledge
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 (2) 32 mph
(3) 20 mph (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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