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 (in minutes) in which the water bed could be filled up?
Answers
Given : A and D inlets are used, the water bed fills up in 20 minutes
B, C, and D are used, the water bed fills up in 15 minutes
A, B, and C are used, it takes 12 minutes to fill up the system
To Find : fastest time in minutes in which the water bed could be filled up
a) 4
b) 10
c) 14
d) 9
Solution:
fastest time is when all pipes opened together.
1/A + 1/D = 1/20 Eq1
1/B + 1/C + 1/D = 1/15 Eq2
1/A + 1/B + 1/C = 1/12 Eq3
Eq3 - Eq2
=> 1/A -1/D = 1/12 - 1/15
=> 1/A - 1/D = (5 - 4)/60 = 1/60 Eq4
Eq1 + Eq4
=> 1/A + 1/A = 1/20 + 1/60
=> 2/A = (3 + 1)/60 = 4/60
=> 1/A = 2/60
=> 1/A= 1/30
1/A + 1/B + 1/C + 1/D = 1/30 + 1/15
=> 1/A + 1/B + 1/C + 1/D = (1 + 2)/30 = 3/30
=> 1/A + 1/B + 1/C + 1/D = 1/10
Hence all pipe together can fill in 10 minutes
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