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Pipe A can fill a tank in 12 hours and Pipe B can fill it in 18 hours. If both pipes are opened together with a drainage pipe C that can empty the full tank in 36 hours, how long will it take to fill the empty tank completely?
8 hours
9 hours
10 hours
12 hours
9 hours
Given: Pipe A fills tank in 12 h, Pipe B fills in 18 h, Drain C empties tank in 36 h
Pipe A fills tank in 12 h, Pipe B fills in 18 h, Drain C empties tank in 36 h
Net rate=121+181−361
Use LCM of 12, 18 and 36 (which is 36) to convert all rates to 36ths and add/subtract instantly
Forgetting to subtract the draining pipe’s rate, which leads to a shorter (incorrect) time
Find individual rates
The filling rate of each pipe is the reciprocal of its time. So A = 1/12 tank/h, B = 1/18 tank/h, C = -1/36 tank/h.
rA=121,rB=181,rC=−361
Compute combined net rate
Add the two filling rates and subtract the draining rate.
rnet=121+181−361=364=91 tank/h
Calculate total time
Time = 1 ÷ net rate.
t=rnet1=911=9 h
B is correct because the net filling rate is 91 tank per hour, giving a total time of 9 hours
Rate‑addition ideas also appear in distance‑speed problems and mixture questions; always express each rate with a common denominator before combining