Question : Pipes A and B running together can fill a cistern in 6 minutes. If B takes 5 minutes more than A to fill the cistern, then what will be the respective time in which A and B will fill the cistern separately?
Option 1: 15 min and 10 min
Option 2: 15 min and 20 min
Option 3: 25 min and 20 min
Option 4: 10 min and 15 min
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Correct Answer: 10 min and 15 min
Solution : Let the time taken by A to fill the cistern be $x$ minutes. So, the time taken by B to fill the cistern is $x+5$ minutes. Time taken by A and B to fill the cistern = 6 minutes Part of cistern filled by A and B in a minute $= \frac{1}{6}$ Part of cistern filled by A in a minute $= \frac{1}{x}$ Part of cistern filled by B in a minute $=\frac{1}{x+5}$ Part of cistern filled by A and B together in a minute $= \frac{1}{x}+\frac{1}{x+5}$ ⇒$\frac{1}{x}+\frac{1}{x+5}=\frac{1}{6}$ ⇒ $12x+30=x^2+5x$ ⇒ $x^2-7x-30=0$ ⇒ $x=-3,10$ $\therefore x=10$ (–3 is neglected because time can't be negative) Time taken by B = 10 + 5 = 15 min Hence, the correct answer is '10 min and 15 min'.
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Question : Two pipes A and B can fill a cistern in $12 \frac{1}{2}$ hours and 25 hours, respectively. The pipes were opened simultaneously, and it was found that, due to leakage in the bottom, it took one hour 40 minutes more to fill the cistern. If the cistern is full, in how much time (in hours) will the leak alone empty 70% of the cistern?
Option 1: 40
Option 2: 35
Option 3: 30
Option 4: 50
Question : Pipes A and B can fill a tank in 12 minutes and 15 minutes, respectively. The tank when full can be emptied by pipe C in $x$ minutes. When all three pipes are opened simultaneously, the tank is full in 10 minutes. The value of $x$ is:
Option 1: 18
Option 2: 15
Option 3: 20
Option 4: 24
Question : Two pipes can fill a tank in 20 minutes and 30 minutes, respectively. When the tank was empty, the two pipes were opened. After some time, the first pipe was stopped, and the tank was filled in 18 minutes. After how much time had passed since the start, was the first pipe stopped?
Option 1: 5 minutes
Option 2: 8 minutes
Option 3: 10 minutes
Option 4: 12 minutes
Question : Two pipes A and B can fill a tank in 12 minutes and 24 minutes, respectively, while a third pipe C can empty the full tank in 32 minutes. All three pipes are opened simultaneously. However, pipe C is closed 2 minutes before the tank is filled. In how much time (in minutes) will the tank be full?
Option 1: 9
Option 2: 10
Option 3: 12
Option 4: 8
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