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?

Solution(By Examveda Team)

$$\eqalign{ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{(Total Capacity)}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{120}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\overline { \downarrow \,\,\,\,\,\,\,\,\,\, \downarrow \,\,\,\,\,\,\,\,\,\,\, \downarrow \,\,\,\,\,\,\,\,\,\,\,\,\, \downarrow } \cr & {\text{efficiency 30}}\,\,\,\,\,\,15\,\,\,\,\,\,\,\,10\,\,\, - 12 \cr & {\text{hours}} \to \,\,\mathop 4\limits_{\left( {\text{P}} \right)}^ \downarrow \,\,\,\,\,\,\mathop 8\limits_{\left( {\text{Q}} \right)}^ \downarrow \,\,\,\,\,\,\,\mathop {12}\limits_{\left( {\text{R}} \right)}^ \downarrow \,\,\,\,\,\,\,\,\,\,\,\mathop {10}\limits_{\left( {\text{S}} \right)}^ \downarrow \cr} $$
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