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 is
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 is
1). 5
2). 10
3). 15
4). 20
1 answers
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