- 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
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 : (x+4) / (x+9)
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 = 48x/9 km/hr.
=> But we know that the ratio of Yana's and Gupta's speeds are 1 : (x+4) / (x+9)
=> Therefore, 48 : 48x/9 :: 1 : (x+4) / (x+9)
Or x/9 = (x+4) / (x+9)
=> x2 + 9x = 9x + 36
=> x2 = 36 or x = 6 hours.
Hence, speed of Gupta = 48x / 9 = 48*6 / 9 = 32 kmph = 20mph
