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
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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