84.
By walking at 3/4th of his usual speed, a man reaches office 20 minutes later than usual. What is his usual time?
Solution:
3/4 of a man's usual speed means, he takes 4/3 of his usual time to cover the same distance, i.e. he takes 4/3 – 1 = 1/3 time extra.
1/3 time is 20 minutes (given)
Usual time = 20 * 3 = 60 minutes. 
87. 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?
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.
