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Pipes K and L can fill a cistern in 8 minutes and 12 minutes respectively. Pipe K is opened at 6 am and closed at 7 am and again opened at 8 am for one hour. Pipe L is opened at 6:30 am and closed at 7:30 am and again opened at 8:30 am for one hour. How long will it take for the cistern to be filled?

Pipes K and L can fill a cistern in 8 minutes and 12 minutes respectively. Pipe K is opened at 6 am and closed at 7 am and again opened at 8 am for one hour. Pipe L is opened at 6:30 am and closed at 7:30 am and again opened at 8:30 am for one hour. How long will it take for the cistern to be filled? Correct Answer 9 hr

Given:

Pipes K can fill the tank = 8 minutes

Pipe L can fill a tank = 12 minutes

Pipe K is opened at 6 am and closed at 7 am and again opened at 8 am for one hour. Pipe L is opened at 6:30 am and closed at 7:30 am and again opened at 8:30 am for one hour.

Formula used:

Total capacity = LCM

Efficiency = Total Capacity/Time

Calculation:

Part of tank pipe K will fill from 6 am to 7 am = 1/8

Part of tank pipe K will fill from 8 am to 9 am = 1/8

Part of tank pipe L will fill from 6:30 am to 7:30 am = 1/12

Part of tank pipe L will fill from 8:30 am to 9:30 am = 1/12

Tank filled till 10 am = 1/8 + 1/8 + 1/12 + 1/12 = 5/12

Tank filled till 2 pm = (5/12) + (5/12) = 10/12 = 5/6

From 2 pm to 2:30 pm, K will fill 1/16 of the tank.

From 2:30 pm to 3 pm, K and L will fill 1/16 + 1/24 part = 5/48 part

Total filled till 3 pm = 5/6 + 1/16 + 5/48 = 1

Hence, the tank will be filled at 3 pm.

Required time to fill the tank = 6 : 00 A.M to 3 : 00 P.M = 9 hrs

∴ The required time to fill the tank is 9 hrs

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