InterviewSolution
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A swimming pool has 3 pipes to drain off the water. The first two pipes A and B, operating simultaneously, can empty the pool in 9/16 the time than that taken by C alone. Pipe A, working alone, takes one third the time taken by pipe B. All of them together take 2 hrs 24 minutes to empty the pool. Time taken by pipe A to empty the pool in hours is1). 52). 103). 154). 20 |
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Answer» Let the efficiencies of the THREE pipes be a, b and c. As the first two pipes A and B OPERATING simultaneously can empty the pool in 9/16 the time than that taken by C alone ⇒ (a + b)/c = 16/9- - - - - - - - - - - - - - - (i) Pipe A, working alone, takes one third the time taken by pipe B ⇒ a/b = 3- - - - - - - - - - - - - - - (ii) 2hr 24min = 2 + 24/60 hr = 2 + 2/5 hour = 12/5 hr Together they can empty the pool in 12/5 hr ⇒ (a + b + c) × 12/5 = 1[Using (ii)] ⇒ (a + a/3 + (a + b) × 9/16) × 12/5 = 1[Using (i)] ⇒ (a + a/3 + (a + a/3) × 9/16) × 12/5 = 1[Using (ii)] ⇒ (a + a/3 + 4a/3 × 9/16) × 12/5 = 1 ⇒ (a + a/3 + 3a/4) = 5/12 ⇒ a(12 + 4 + 9)/12 = 5/12 ⇒ a = 1/5 Since the efficiency of pipe A is a, the time taken by A alone = 1/a = 5 hours |
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