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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