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Pipes A and B can fill a tank in 8 hours and 10 hours, respectively, and pipe C can empty the full tank in 12 hours. All three pipes are opened together, but pipe A is closed after 4 hours. In how many hours will the remaining part of the tank be filled?
30
22
24
26
26
Use LCM of (8, 10, 12) = 120 units as total capacity. Efficiencies are A=15, B=12, C=10. Net efficiency (A+B-C) = 17. After 4 hours, work done = 17 ├Ч 4 = 68 units. Remaining = 120 - 68 = 52. Pipe A closes, leaving B and C with net efficiency (12 - 10) = 2. Time = 52 / 2 = 26 hours.
Pipes A, B, and C fill/empty a tank in 8, 10, and 12 hours respectively. A and B are filling pipes, C is an emptying pipe. All work for 4 hours, then A is closed.
Total┬аWork=Time├ЧEfficiency, EfficiencynetтАЛ=EAтАЛ+EBтАЛтИТECтАЛ
Use LCM of (8, 10, 12) = 120 units as total capacity. Efficiencies are A=15, B=12, C=10. Net efficiency (A+B-C) = 17. After 4 hours, work done = 17 ├Ч 4 = 68 units. Remaining = 120 - 68 = 52. Pipe A closes, leaving B and C with net efficiency (12 - 10) = 2. Time = 52 / 2 = 26 hours.
Many students forget that pipe C continues to empty the tank even when pipe A is closed, leading to incorrect net efficiency.
Calculate Total Capacity and Individual Efficiencies
Find the LCM of 8, 10, and 12, which is 120. Efficiencies are: A = 120/8 = 15, B = 120/10 = 12, C = 120/12 = 10 (emptying).
EAтАЛ=15,EBтАЛ=12,ECтАЛ=тИТ10
Work done in the first 4 hours
All three pipes (A, B, C) are open for 4 hours. The combined net efficiency is 15 + 12 - 10 = 17 units/hour.
Work4hrтАЛ=(15+12тИТ10)├Ч4=17├Ч4=68
Remaining work and time taken
Remaining work is 120 - 68 = 52 units. After A is closed, only B and C work. Net efficiency is 12 - 10 = 2 units/hour.
TimeremтАЛ=12тИТ1052тАЛ=252тАЛ=26┬аhours
D is correct because the remaining 52 units of work are completed by pipes B and C at a net rate of 2 units per hour, taking 26 hours.
This concept is identical to work-sharing problems where an individual leaves halfway; always subtract the completed portion of the work first.
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