Question

A pipe A can fill a tank in 6 hours and pipe B can empty the full tank in 8 hours. If both pipes are opened together, the tank will be filled in

• A. 20 hours
• B. 18 hours
• C. 24 hours
• D. 12 hours

Hint:

Subtract the emptying rate from the filling rate to get the net rate, then invert.

Answer 1

The Correct Option is C

Step 1: Rates of the two pipes.
A fills \(\dfrac{1}{6}\) per hour; B empties \(\dfrac{1}{8}\) per hour.
Step 2: Net rate.
\(\dfrac{1}{6}-\dfrac{1}{8}=\dfrac{4-3}{24}=\dfrac{1}{24}\) per hour.
Step 3: Time to fill.
\(24\) hours.
\[\boxed{24\ \textrm{hours}}\]