Question 8.
Three pipes 'A', 'B' and 'C' take 12 min, 20 min and 15 min more than an hour respectively to fill a tank. All the three pipes are opened together for 12 min
to try to fill the same tank. Then, 'C' is closed. After another 16 min, there occurs a leakage in 'A' and the tank is fully filled after 4 min 20 sec. What
percentage of A's throughput is lost due to the leakage?
Pick ONE option
A) 25%
B) 22%
C) 18%
D) 20%
Answers
Given : Three pipes 'A', 'B' and 'C' take 12 min, 20 min and 15 min more than an hour respectively to fill a tank. All the three pipes are opened together for 12 min to try to fill the same tank. Then, 'C' is closed. After another 16 min, there occurs a leakage in 'A' and the tank is fully filled after 4 min 20 sec
To find : What percentage of A's throughput is lost due to the leakage?
Solution:
Pipe A takes 12 mins more than 1 hr = 72 Min
Pipe B takes = 80 min
Pipe C takes = 75 min
All together fill in 1 min = 1/72 + 1/80 + 1/75
= ( 50 + 45 + 48)/3600
= 143/3600
Filled in 12 mins = 12 * 143/3600 = 143/300
Remained = 1 - 143/300 = 157/300
pipe A & B in 1 Min = 1/72 + 1/80 = 19/720
in 16 min = 16 * 19/720 = 19/45
Remained = 157/300 - 19/45
= ( 471 - 380)/900
= 91/900
Filled in 4 min 20 sec further = 91/900
To be filled in 4 min 20 secs if no leakage = (13/3) (19/720)
= 247/2160
Leakage = 247/2160 - 91/900
= (1235 - 1092)/10800
= 143/10800
A to be filled in 13/3 Mins
= (1/72)(13/3)
= 13/216
% Leakage = 100 * ( 143/10800) / ( 13/216)
= 100 * 143 * 216 / ( 13 * 108)
= 11 * 2
= 22 %
22 % of A's throughput is lost due to the leakage
option B is correct
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