Rishi has set up hydroponics on his terrace. He has connected the water bed to four water inlets A,B,C,D. The problem is that water flow from all these inlets is not the same. If A and D inlets are used, the water bed fills up in 20 minutes. If B, C, and D are used, the water bed fills up in 15 minutes. If A, B, and C are used, it takes 12 minutes to fill up the system. If Rishi was in a rush, what is the fastest time inminutes in which the water bed could be filled up?
A. 14
B. 10
C. 14
D. 9
Answers
Solution :-
→ LCM of 20,15 and 12 = 60 units = Let capacity of water bed .
so,
→ Efficiency of (A + D) = Capacity / Time taken = 60/20 = 3 units / min. --------- Eqn.(1)
→ Efficiency of (B + C + D) = Capacity / Time taken = 60/15 = 4 units / min. --------- Eqn.(2)
→ Efficiency of (A + B + C) = Capacity / Time taken = 60/12 = 5 units / min. --------- Eqn.(3)
now, from Eqn.(1) ,
- D = 2 or 1 .
if D = 2 ,
- B and C are 1 in Eqn.(2) . => 1 + 1 + 2 only possible.
then, in Eqn.(3),
- A + 1 + 1 = 5
- A = 3 which is not possible in Eqn.(1)
therefore,
- D = 1 .
- from eqn.(3) we get (A + B + C) + D = 5 + 1 = 6 units / min.
hence,
→ Total time taken by (A + B + C + D) to fill the water bed = 60 / 6 = 10 days. (Ans.)
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