Question : Two pipes A and B can fill a tank in 12 hours and 18 hours, respectively. Both pipes are opened simultaneously. In how much time will the empty tank be filled completely?
Option 1: 9 hours 30 minutes
Option 2: 8 hours
Option 3: 7 hours 12 minutes
Option 4: 10 hours 24 minutes
Correct Answer: 7 hours 12 minutes
Solution :
Hourly work of pipe A = $\frac{1}{12}$
Hourly work of pipe B = $\frac{1}{18}$
Hourly work of pipe A and B = $\frac{1}{12}+\frac{1}{18}$
= $\frac{15+10}{180}$
= $\frac{25}{180}$
= $\frac{5}{36}$
Thus, the tank can be filled completely in $\frac{36}{5}$ hrs = 7.2 hrs = 7 hours 12 minutes
Hence, the correct answer is '7 hours 12 minutes'.
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