Question
Download Solution PDFA cistern is filled by two taps A and B in 3 hrs and 7 hrs respectively. The full cistern can be emptied by the third tap C in 6 hrs. If all the taps be opened at the same time, in how much time will the empty tank be filled up completely?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Tap A fills the cistern in 3 hours.
Tap B fills the cistern in 7 hours.
Tap C empties the cistern in 6 hours.
Formula used:
Net filling rate = (Rate of A + Rate of B - Rate of C)
Time to fill the cistern = 1 / Net filling rate
Calculation:
Rate of A = 1 / 3
Rate of B = 1 / 7
Rate of C = -1 / 6
Net filling rate = (1 / 3) + (1 / 7) - (1 / 6)
⇒ Net filling rate = (14 + 6 - 7) / 42
⇒ Net filling rate = 13 / 42
Time to fill the cistern = 1 / (13 / 42)
⇒ Time to fill the cistern = 42 / 13
⇒ Time to fill the cistern = 33/13 hours
∴ The correct answer is option (3).
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