Question

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?​

Answer 1

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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