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# Arithmetic Aptitude :: Pipes & Cistern

## 3. Pipe A can fill a tank in 8 hours and Pipe B can fill it in 6 hours. If both the pipes are opened but after 2 hours pipe A is closed, then the other pipe will fill the tank in

Explanation :

Tank part filled by Pipe A in 1 hour = 1/8
or
Time taken to fill 1/8 part of tank filled A = 1 hour ------------- (1)

Tank part filled by Pipe B in 1 hours = 1/6
or
Time taken to fill 1/6 part of tank filled B = 1 hour ---------(2)

=> Tank Part filled by (A+B) in 1 hour = (1/8 + 1/6)

=> Tank Part filled by (A+B) in 2 hour = 2*(1/8 + 1/6) = 2*(3+4)/24 = 2*7/24 = 7/12

After 2 hours left over portion of tank = (1-7/12) = 5/12

Time taken to fill 1/6 part of tank filled B = 1 hour
so time taken to fill 5/12 part of tank by B = 6 * 5/12 = 5/2 = 2 1/2
=> So it takes 2 1/2 hrs (2hrs 30 min) to fill 5/12 of tank.