Q) In the bottom of a water tank, there are two drains A and B. If only A is open, it takes 30 minutes to empty a full tank and if only B is open, it takes 20 minutes. If for 10 minutes both drains are open, then B is closed, how much time it takes to empty a full tank?

a) 18 minutes                            b) 15 minutes

c) 17 minutes                            d) 20 minutes

Ans:

Method 1:

Time taken by A to drain water tank = 30 min

Time taken by B to drain water tank = 20 min

∴ Work done by A in 1 min = 1/30

∴ Work done by B in 1 min = 1/20

∴ Work done by A & B together in 1 min = 1/30 + 1/20 = 5/60 = 1/12

∴ Work done by A & B together in 10 min = 1/12 x 10 = 5/6

∴ Balance work = 1 – 5/6 = 1/6

Since this work is done by A now @ 1/30 work per min

∴ Time to empty the tank = (1/6)/(1/30) = 5 mins

Total time taken to empty the tank = Time taken by both A and B + Time taken by A

= 10 + 5 = 15 mins

Method 2:

Let A and B be the work done by drain A and drain B respectively in 1 min

Work done by A & B together in 10 mins = 10 (A + B)

Let’s consider drain A takes X mins, hence, work done by A = XA

Total work done: XA + 10 (A + B) = 1

Since A is 1/30 and B = 1/20

∴ X (1/30) + 10 (1/30 + 1/20) = 1

∴ X/30 + 50/60 = 1

∴ 2X + 50 = 60 =>  X = 5 mins

Total time taken to empty the tank = Time taken by both A and B + Time taken by A

= 10 + 5 = 15 mins