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Pipe A can fill a tank in 5 hours. Pipe B can empty it in 12 hours. If both the pipes are opened simultaneously, how much time will it take to fi
Question

Pipe A can fill a tank in 5 hours. Pipe B can empty it in 12 hours. If both the pipes are opened simultaneously, how much time will it take to fill the tank?

A.

827 hours8 \frac{2}{7} \text{ hours} \quad​​

B.

847 hours8 \frac{4}{7} \text{ hours} \quad​​

C.

817 hours 8 \frac{1}{7} \text{ hours} \quad​​

D.

837 hours8 \frac{3}{7} \text{ hours}​​

Correct option is B

Given:

Pipe A can fill the tank in 5 hours.

Pipe B can empty the tank in 12 hours.

Formula Used:

Rate of work =1Time \frac{1}{\text{Time}}​​

Time taken =1Net rate of work \frac{1}{\text{Net rate of work}}​​

Solution:
Rate of work of Pipe A =15=\frac{1}{5}​ (since it fills the tank in 5 hours)
Rate of work of Pipe B = 112-\frac{1}{12}​ (since it empties the tank in 12 hours)

Net rate of work =15112 \frac{1}{5} - \frac{1}{12}​​

Net rate of work =1260560=760 \frac{12}{60} - \frac{5}{60} = \frac{7}{60}​​

Now, time taken to fill the tank =1760=607=847= \frac{1}{\frac{7}{60}} = \frac{60}{7} = 8\frac 47 hours

Alternate Method:

Time taken to fill the tank = 60125=607=847\frac {60}{12-5}=\frac {60}7=8\frac47 hours​

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