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P, Q and R are 3 small pumps fitted to a tank. S is a large pump

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P, Q and R are 3 small pumps fitted to a tank. S is a large pump  [#permalink]

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New post 09 Dec 2019, 10:26
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A
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E

Difficulty:

  65% (hard)

Question Stats:

46% (02:56) correct 54% (03:09) wrong based on 24 sessions

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P, Q and R are 3 small pumps fitted to a tank. S is a large pump fitted to the tank. Q is 50% more efficient than P. R is 100/3% is more efficient than Q. S is 50% more efficient than R. All of the pumps are used to fill the tank.
What is the ratio of the time taken by pumps P and R to fill the tank together to the time taken by pumps Q and S to fill the tank together ?

A. 3 : 2
B. 4 : 3
C. 2 : 3
D. 3 : 5
E. 3 : 4

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Re: P, Q and R are 3 small pumps fitted to a tank. S is a large pump  [#permalink]

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New post 09 Dec 2019, 21:06
efficiency of P= x
efficiency of Q= \(\frac{3x}{2}\)
efficiency of R= \(\frac{3x}{2}*\frac{4}{3}\)=2x
efficiency of S= 2x*\(\frac{3}{2}\)=3x

E(P+R) : E(Q+S)= 3x : 4.5x= 2:3

T(P+R):T(Q+S)= 3:2

TheNightKing wrote:
P, Q and R are 3 small pumps fitted to a tank. S is a large pump fitted to the tank. Q is 50% more efficient than P. R is 100/3% is more efficient than Q. S is 50% more efficient than R. All of the pumps are used to fill the tank.
What is the ratio of the time taken by pumps P and R to fill the tank together to the time taken by pumps Q and S to fill the tank together ?

A. 3 : 2
B. 4 : 3
C. 2 : 3
D. 3 : 5
E. 3 : 4
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Re: P, Q and R are 3 small pumps fitted to a tank. S is a large pump  [#permalink]

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New post 09 Dec 2019, 21:29
TheNightKing wrote:
P, Q and R are 3 small pumps fitted to a tank. S is a large pump fitted to the tank. Q is 50% more efficient than P. R is 100/3% is more efficient than Q. S is 50% more efficient than R. All of the pumps are used to fill the tank.
What is the ratio of the time taken by pumps P and R to fill the tank together to the time taken by pumps Q and S to fill the tank together ?

A. 3 : 2
B. 4 : 3
C. 2 : 3
D. 3 : 5
E. 3 : 4

rate of Q = 3/2 (rate of P)
rate of R = 4/3 (rate of Q) = (4/3) (3/2) (rate of P) = 2 * rate of P
rate of S = 3/2 (rate of R) = (3/2) (2 * rate of P) = 3 * rate of P

required ratio = (rate of Q + rate of S) / (rate of P + rate of R)
= ( 3/2 + 3) / (1 + 2) = 3 : 2

A is correct
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Re: P, Q and R are 3 small pumps fitted to a tank. S is a large pump  [#permalink]

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New post 09 Dec 2019, 21:54
TheNightKing wrote:
P, Q and R are 3 small pumps fitted to a tank. S is a large pump fitted to the tank. Q is 50% more efficient than P. R is 100/3% is more efficient than Q. S is 50% more efficient than R. All of the pumps are used to fill the tank.
What is the ratio of the time taken by pumps P and R to fill the tank together to the time taken by pumps Q and S to fill the tank together ?

A. 3 : 2
B. 4 : 3
C. 2 : 3
D. 3 : 5
E. 3 : 4


Avoid fractions by assuming a convenient value for the rate of P. Say it pumps 4 lt/sec.

P = 4 lts/sec
Q = 50% more efficient than P = 6 lts/sec
R = 100/3% more efficient that Q = 8 lts/sec
S = 50% more efficient than R = 12 lts/sec

Rate of P and R together = 4 + 8 = 12
Rate of Q and S together = 6 + 12 = 18

Ratio of rates of P and R : Q and S = 2:3 so ratio of time taken by them will be inverse i.e. 3 : 2.

Answer (A)
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Re: P, Q and R are 3 small pumps fitted to a tank. S is a large pump   [#permalink] 09 Dec 2019, 21:54
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