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Bucket P has thrice the capacity as bucket Q. It takes 60 turns for bucket P to fill the empty drum. How many turns it will take for both the buckets P and Q having each turn together, to fill the empty drum?

A 30
B 40
C 45
D 60
E 90

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Sun Jun 03, 2018 11:05 am

vaibhav101 wrote:Bucket P has thrice the capacity as bucket Q. It takes 60 turns for bucket P to fill the empty drum. How many turns it will take for both the buckets P and Q having each turn together, to fill the empty drum?

A 30
B 40
C 45
D 60
E 90

Let Q = 1 liter per turn.
Since P has 3 times the capacity of Q, P = 3 liters per turn.
Since P takes 60 3-liter turns to fill the drum, the drum = 60*3 = 180 liters.
Since P = 3 liters per turn and Q = 1 liter per turn, the number of turns for P and Q together to fill the 180-liter drum = 180/(3+1) = 45.

The correct answer is C.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 7243; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Tue Jun 05, 2018 9:40 am

vaibhav101 wrote:Bucket P has thrice the capacity as bucket Q. It takes 60 turns for bucket P to fill the empty drum. How many turns it will take for both the buckets P and Q having each turn together, to fill the empty drum?

A 30
B 40
C 45
D 60
E 90

We see the rate of bucket P is 1/60. Since bucket P has thrice the capacity as bucket Q, it will take 180 turns for bucket Q to fill the empty drum. Thus the rate of bucket Q is 1/180. Therefore, their combined rate is 1/60 + 1/180 = 3/180 + 1/180 = 4/180 = 1/45. Thus it will take them 1/(1/45) = 45 turns if they work together to fill the empty drum.

rate of 3 + 1 = 4 gallons per turn; thus, it will take them 180/4 = 45 turns to complete the fill.

Answer: C

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