Directions: In the following question, two quantities A and B are given. You have to use your knowledge of mathematics to find the values of both A and B and choose the most appropriate relationship between the magnitudes of A and B from the given options.

Quantity A: Pipes X and Y can fill a tank in 15 hours and 20 hours respectively. There is a hole at 3/4th of the height of the tank which can drain water in 12 hours if it is at the bottom of the tank. How much time will it take to fill the tank?

Quantity B:  14 hours.

Quantity A -

Let the volume of tank = LCM of (15, 20, 12) = 60 units.

X's capacity = 60 / 15 = 4 units.

Y's capacity = 60 / 20 = 3 units.

Hole's emptying capacity = 60 / 12 = 5 units.

Time taken to fill (3 / 4)th tank = 45 / (4 + 3) = 6.42 units

Time taken for remaining (1 / 4)th tank = 15 / (4 + 3 - 5) = 7.5 units

Total time = 6.42 + 7.5 = 13.92 hours

Quantity B - 14 hours.

Hence, Quantity A < Quantity B

Confusion Points The statement that a hole at the bottom would have caused the tank to empty in 12 hours was made to give readers a sense of the pipe's flow rate, not to imply that the hole is at the bottom.