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Examoogle • User • info@examoogle.com • EE-2024-8821
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A tap can fill a tank in 48 minutes, whereas another tap can empty it in 2 hours. If both the taps are opened at 11:40 A.M., at what time will the tank be filled?
35 P.M.
00 P.M.
30 P.M.
12:40 P.M.
00 P.M.
Given: Tap A fills the tank in 48 minutes. Tap B empties the tank in 2 hours (120 minutes). Start time is 11:40 A.M.
Tap A fills the tank in 48 minutes. Tap B empties the tank in 2 hours (120 minutes). Start time is 11:40 A.M.
T=RA−RBW
Use LCM of 48 and 120 (which is 240 units). Efficiency of A = +5 units/min, Efficiency of B = -2 units/min. Net = 3 units/min. Time = 240 / 3 = 80 minutes.
Confusing 2 hours as 2 minutes or forgetting to convert hours to minutes; failing to realize that an 'emptying' tap must be subtracted from the filling tap's rate.
Convert all units to minutes
Convert the emptying time from hours to minutes: 2 hours=2×60=120 minutes.
TB=120 min
Calculate Work and Efficiencies
Take the LCM of 48 and 120 to find total capacity: LCM(48,120)=240 units. Efficiency of tap A (EA) = 240/48=5 units/min. Efficiency of tap B (EB) = 240/120=2 units/min (negative as it empties).
Enet=5−2=3 units/min
Find Time to Fill
Divide total capacity by net efficiency: 240/3=80 minutes.
T=80 min=1 hour 20 minutes
Calculate Final Clock Time
Add 1 hour and 20 minutes to 11:40 A.M. Adding 20 minutes reaches 12:00 P.M. (noon). Adding the remaining 1 hour results in 1:00 P.M.
11:40 A.M.+1 hr 20 min=01:00 P.M.
B is correct because adding 80 minutes (1 hour 20 minutes) to 11:40 A.M. results in 1:00 P.M.
This 'net-efficiency' approach is identical to solving problems involving relative speed in trains moving in opposite directions.