Pipes and Cisterns Practice Test 3 with solutions

Question : 4 of 7

Marks: +1, -0

A tank can be filled separately by two taps A and B in 45 minutes and 36 minutes respectively. A tap C at the bottom can empty the full cistern in 30 minutes. If the tap C is opened 7 minutes after the two taps A and B are opened, find when the cistern will be full?

46 minutes
25 minutes
14 minutes
None of these

Validate

Solution:

In 7 minutes (A + B) together will fill = 7 ×

(1/{45}+1/{36})

7 × 1/{20}

7/{20}

tank
Unfilled portion of tank after 7 minutes = 1 -

7/{20}

{13}/{20}

tank
Now, tank filled in 1 minute when A, B and C are opened =

1/{45}+1/{36} - 1/{30}

1/{60}

∴ Time required to fill

{13}/{30}

tank =

60 × {13}/{20}

= 39 minutes
Hence, total time required to fill the tank = 7 + 39 = 46 minutes.

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