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Tap A and B can fill the tank in 20 hours and 25 hours respectively. Tap C and D can empty the tank in 40 hours and 60 hours respectively. Tap A and B opened till half of the tank is filled. Then, tap A, B and C opened to fill 1/4th of tank gets filled. To fill remaining tank, all four taps are opened. Approximately, in what time tank will completely filled?

Tap A and B can fill the tank in 20 hours and 25 hours respectively. Tap C and D can empty the tank in 40 hours and 60 hours respectively. Tap A and B opened till half of the tank is filled. Then, tap A, B and C opened to fill 1/4th of tank gets filled. To fill remaining tank, all four taps are opened. Approximately, in what time tank will completely filled? Correct Answer 14.4 hours

Calculation:

Tap A's 1 hour's work = 1/20

Tap B's 1 hour's work = 1/25

Tap C's 1 hour's work = 1/40

Tap D's 1 hour's work = 1/60

Tap (A + B)'s 1 hours work = 1/20 + 1/25 = 9/100

Time taken by A and B to complete half of the work = 1/2 × 100/9 = 50/9 = 5.5 hours

Tap (A + B + C)'s 1 hours work = 1/20 + 1/25 - 1/40 = 13/200

Time taken by A, B and C to fill 1/4th of tank = 1/4 × 200/13 = 50/13 = 3.8 hours

Remaining work = 1 - 1/2 - 1/4 = 1/4

Tap(A + B + C + D)'s 1 hours work = 1/20 + 1/25 - 1/40 - 1/60 = 29/600

Time taken four taps to fill 1/4th tank = 1/4 × 600/29 = 150/29 = 5.1 hours

∴ Required time = 5.5 + 3.8 + 5.1 = 14.4 hours

Important Points

Duration of time when different taps are opened for different times.

Fraction of tank filled × (1/taps 1 hours work) = Time in which fraction of tank gets filled

Related Questions

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