1.

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

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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