Multiple choice

Three pipes P, Q and R can fill a tank in 6 hours, after working it at together for 2 hours, R is closed and P and Q can fill the remaining part in 7 hours. How much time will R take alone to fill the tank?

  1. 16 hours

  2. 14 hours

  3. 12 hours

  4. 10 hours

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let P, Q, R together fill in 6 hours. Their combined rate = 1/6 per hour. In 2 hours, they fill 2/6 = 1/3 of tank. Remaining = 2/3. P and Q fill 2/3 in 7 hours, so their combined rate = (2/3)/7 = 2/21 per hour. Therefore R's rate = (1/6) - (2/21) = (7/42) - (4/42) = 3/42 = 1/14 per hour. So R alone takes 14 hours.

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