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Three pipes X, Y and Z can fill a pool in 12, 15 and 20 hours respectively. If pipe X is open all the time and pipe Y and pipe Z are open for 1 hour each alternatively, what will be the total hours required to full the pool?
  • a)
    6 hours
  • b)
    hours
  • c)
    7 hours
  • d)
    hours
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Three pipes X, Y and Z can fill a pool in 12, 15 and 20 hours respecti...
Given:
Pipes X, Y, and Z can fill a pool in 12, 15, 20 hours respectively.
Concept:
If a tap can fill a tank in x hours, then the tank filled by the tap in 1 hour = 1/x of the total tank.
Calculation:
Part filled by X and Y in 1 hours
⇒ (1/12) + (1/15)
⇒ (5 + 4)/60
⇒ 9/60
⇒ 3/20 ----(1)
Part filled by X and Z in the next 1 hours
⇒ (1/12) + (1/20)
⇒ (5 + 3)/60
⇒ 8/60
⇒ 2/15
Part filled in 2 hours = (3/20) + (2/15)
⇒ (9 + 8)/60
⇒ 17/60
Part filled in 6 hours = 3 × 17/60 = 17/20
Remaining part = 1 – (17/20)
⇒ 3/20
This part will be filled by (X + Y) in 1 hour by eq. (1)
Total time = 6 + 1 = 7 hours
∴ The required time is 7 hours.
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