Three pipes A, B and C can fill a tank in 16 hours. After working together for 4 hours, pipe B is closed and the remaining part is filled by pipe A and C in 18 hours. If the efficiency of pipe B is 1.5 times of the efficiency of pipe C, then in how much time can pipe A fill the tank alone?
Answers
Given : Three pipes A, B and C can fill a tank in 16 hours.
After working together for 4 hours, pipe B is closed and the remaining part is filled by pipe A and C in 18 hours.
The efficiency of pipe B is 1.5 times of the efficiency of pipe C,
To Find: in how much time can pipe A fill the tank alone
Solution:
A can fill in 1 day = A
C can fill in 1 day = C
efficiency of pipe B is 1.5 times of the efficiency of pipe C
=> B can fill in 1 day = 1.5C
Three pipes A, B and C can fill a tank in 16 hours
=> 16A + 16B + 16C = W (Total work)
=> 16A + 16(1.5C) + 16C = W
=> 16A + 40C = W
Work done in 4 hrs
= 4A + 4B + 4C = 4A + 4(1.5C) + 4C = 4A + 10C
Remaining work = 16A + 40C - (4A + 10C)
= 12A + 30C
pipe A and C in 18 hours. = 18A + 18C
18A + 18C = 12A + 30C
=> 6A = 12C
=> A = 2C
16A + 40C = W
=> 16A + 20A = W
=> 36A = W
Hence pipe A fill the tank alone in 36 hrs
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