Question : Pipe A can fill 50% of the tank in 6 hours and Pipe B can fill the same tank in 18 hours. If both the pipes are opened simultaneously, how much time (in minutes) will the empty tank be filled?
Option 1: 420
Option 2: 425
Option 3: 432
Option 4: 435
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Correct Answer: 432
Solution :
Time taken by A to fill half the cistern = 6 hours
Time taken by A to fill the full cistern = 12 hours
Time taken by B to fill the cistern = 18 hours
Part filled by A in one hour = $\frac{1}{12}$
Part filled by B in one hour = $\frac{1}{18}$
Part filled by A and B together in one hour = $\frac{1}{12}+\frac{1}{18}=\frac{5}{36}$
So, time taken by A and B to fill the cistern = $\frac{36}{5}$ hours = 432 minutes
Hence, the correct answer is 432.
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