Two friends A and B decided to work together and fill a pool of capacity 1000 liters. Using a bucket each, A fills at the rate of 4 liters every 3 minutes and B fills at 3 liters every 4 minute. What would be the total time required to fill the pool, given that they take a break of 3 minutes each time both of them put a bucket into the pool at the same instant ?
(A) 6 hours
(B) 10 hours
(C) 8 hours
(D) 9 hours 57 minutes
Answer: (D)
Explanation: We are given that A fills the pool at the rate of 4 liters every 3 minutes and B fills the pool at the rate of 3 liters every 4 minutes.
=> Pool filled by A in 12 minutes = 4 x 4 = 16 liters
=> Pool filled by B in 12 minutes = 3 x 3 = 9 liters
=> Pool filled in 12 minutes = 16 + 9 = 25 liters
or we can say to fill 25 liters water, they will take 12 minutes.
Therefore to fill 1000 liters they will take (12*1000)/25 minutes i.e. 8 hours.
=> Since they will put a bucket at the same instant every 12 minutes. (LCM of 3 and 4 minutes = 12 minutes).
=> After every 12 minutes they will take rest for 3 minutes.
=> Overall (8*60)/12 i.e 40 times they take rest while working .
=> So every 12 minutes should be considered 15 (12+3) minutes for 40 times.
=> But after having taken 39 times . The pool of capacity 1000 liters will be filled.
=> Last 3 minutes must not be considered.
Therefore, to fill 1000 liters (25 x 40 liters), it would take (12*1000)/25 minutes i.e. 8 hours. + (39*3) minutes = 8 hrs. + 117 minutes
So ans is 9 hrs 57 minutes.
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