Question : Tap A can fill an empty tank in 8 hours if no other tap is open, and tap B can empty the same tank, when filled, in 12 hours, when no other tap is open. Find the time taken to fill the same tank, when empty, if both the taps are opened together.
Option 1: 12 hours
Option 2: 16 hours
Option 3: 24 hours
Option 4: 36 hours
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Correct Answer: 24 hours
Solution : Let the rate at which tap A fills the tank as A and the rate at which tap B empties the tank as B. Given that tap A can fill the tank in 8 hours, A = $\frac{1}{8}$ tanks per hour. Similarly, tap B can empty the tank in 12 hours, B = $\frac{1}{12}$ tanks per hour. When both taps are opened together, the net rate of filling the tank = $\frac{1}{8} - \frac{1}{12}=\frac{1}{24}$ tanks per hour. The time is taken to fill the tank when both taps are opened together = $\frac{1}{\frac{1}{24}}$ = 24 hours Hence, the correct answer is 24 hours.
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Question : Pipe A can fill an empty tank in 30 hours and B can fill it in 10 hours. Due to a leakage in the tank, it takes pipes A and B together 1.5 hours more to fill completely than it would have otherwise taken. What is the time taken by the leakage alone to empty the same tank completely, starting when the tank is completely full?
Option 1: 42 hours
Option 2: 40 hours
Option 3: 36 hours
Option 4: 45 hours
Question : Two taps J and L can fill a tank alone in 10 minutes and 12 minutes respectively. If an outlet tap K is opened and all three taps work together, then the same tank will be filled in 15 minutes. How much time will tap K alone take to empty the same tank?
Option 1: $\frac{58}{ 11}$ minutes
Option 2: $\frac{52}{ 3}$ minutes
Option 3: $\frac{60}{7}$ minutes
Option 4: $\frac{56}{3}$ minutes
Question : Pipes A and B together can fill a tank in 10 hours. Pipes B and C together can fill the same tank in 12 hours. Pipes A and C together can fill the same tank in 15 hours. In how many hours can pipe B alone fill the same tank?
Option 1: $\frac{120}{7}$ hours
Option 2: $15$ hours
Option 3: $\frac{120}{11}$ hours
Option 4: $\frac{155}{13}$ hours
Question : Two taps P and Q can fill a tank alone in 10 hours and 12 hours respectively. If the two taps are opened at 9 a.m., then at what time should the tap P be closed to fill the tank at exactly 3 p.m.?
Option 1: 2 p.m.
Option 2: 1 p.m.
Option 3: 3 p.m.
Option 4: 12 p.m.
Question : Pipes P and Q can fill a tank in 12 hours and 36 hours, respectively. If both pipes are opened, then how much time (in hours) will it take to fill the tank?
Option 1: 9
Option 2: 8
Option 3: 10
Option 4: 7
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