Rishi has set up hydroponics on his terrace. He has connected the water bed to four water inlets
A
,
B
,
C
,
D
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
i
n
m
i
n
u
t
e
s
inminutes in which the water bed could be filled up?
Your Answer
a) 4
b) 10
c) 14
d) 9
Please tell me fast urgently
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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