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
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Correct Answer: $\frac{60}{7}$ minutes
Solution : Given: Two taps J and L can fill a tank alone in 10 and 12 minutes respectively. Let the K pipe take $x$ minutes to empty a full tank. Use the formula, (A + B – C)'s 1-hour work = $\frac{1}{A}+\frac{1}{B}–\frac{1}{C}$. According to the question, $\frac{1}{10}+\frac{1}{12}–\frac{1}{x}=\frac{1}{15}$ ⇒ $\frac{1}{x}=\frac{1}{10}+\frac{1}{12}–\frac{1}{15}$ ⇒ $\frac{1}{x}=\frac{6+5–4}{60}$ ⇒ $\frac{1}{x}=\frac{7}{60}$ ⇒ $x=\frac{60}{7}$ minutes Hence, the correct answer is $\frac{60}{7}$ minutes.
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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.
Question : Two pipes can fill a tank alone in 20 hours and 24 hours respectively and an outlet pipe alone can empty 20 gallons of water per hour. All three pipes working together can fill the same empty tank in 40 hours. What is the capacity of the tank?
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