83. A man can row 50 km upstream and 72 km downstream in 9 hours. He can also row 70 km upstream and 90 km downstream in 12 hours. Find the rate of current.

Solution:
Let x and y be the upstream and downstream speed respectively.
Hence 50/x + 72/y = 9 and 70/x + 90/y = 12
Solving for x and y we get x = 10 km/hr and y = 18 km/hr
We know that Speed of the stream = 1/2 * (downstream speed - upstream speed) = 1/2 (18 – 10) = 4 km/hr.

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.