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- Tap X can fill a cistern in 10 minutes and tap Y can fill in 12 minutes.
Question 1:
Tap X can fill a cistern in 10 minutes and tap Y can fill in 12 minutes. There is a leakage in the bottom of the cistern that empties the tank in 24 minutes. If both taps X and Y are opened together, then how long will it take to fill the cistern?
A. 5 5/17 minutes
B. 9 12/17 minutes
C. 2 16/17 minutes
D. 7 1/17 minutes
Feedback Time taken by X to fill the tank = 10 minutes.
Part filled by X in 1 minute = 1/10
Time taken by Y to fill the tank = 12 minutes.
Part filled by Y in 1 minute = 1/12
Time taken by the leakage to empty the tank = 24 minutes.
Part emptied by the leakage in 1 minute = 1/24
Therefore, net part filled by (X + Y + leakage) in 1 minute = 1/10 + 1/12 – 1/24 = (24+20-10)/240 = 34/240 = 17/120.
Time Part of tank filled
1 minute 17/120
? 1 (here 1 denotes completely filled tank)
Time taken to fill the tank = 120/17 x 1 = 7 1/17 minutes.
Part filled by X in 1 minute = 1/10
Time taken by Y to fill the tank = 12 minutes.
Part filled by Y in 1 minute = 1/12
Time taken by the leakage to empty the tank = 24 minutes.
Part emptied by the leakage in 1 minute = 1/24
Therefore, net part filled by (X + Y + leakage) in 1 minute = 1/10 + 1/12 – 1/24 = (24+20-10)/240 = 34/240 = 17/120.
Time Part of tank filled
1 minute 17/120
? 1 (here 1 denotes completely filled tank)
Time taken to fill the tank = 120/17 x 1 = 7 1/17 minutes.
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