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1. Three pipes P, Q and R can separately fill a cistern in 4, 8 and 12 hours respectively. Another pipe S can empty the completely filled cistern in 10 hours. Which of the following arrangements will fill the empty cistern in less time than others?

A. Q alone is open

B. P, R and S are open

C. P and S are open

D. P, Q and S are open

Solution:

\begin{aligned} (Total Capacity) \\ 120 \\ \bar{↓ ↓ ↓ ↓} \\ efficiency 30 15 10 - 12 \\ hours \to 4_{(P)}^{↓} 8_{(Q)}^{↓} 12_{(R)}^{↓} 10_{(S)}^{↓} \end{aligned}

In order to fill the cistern in less time.
So, efficiency of filling should be more
now, check all options
(A) → Q efficiency 15 units/hr
(B) → (P + R - S) efficiency
= 30 + 10 - 12 = 28 units/hr
(C) → (P - S) efficiency
= 30 - 12 = 18 units/hr
(D) → (P + Q - S) efficiency
= 30 + 15 - 12 = 33 units/hr
Option (D) is answer
Since efficiency of option (D) is highest

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