Question

Two pipes A and B can fill a tank in 36 hours and 46 hours respectively. If both the pipes are opened simultaneously, bow much time will be taken to fill the tank?

• A. 20
• B. 25
• C. 35
• D. 30

Answer 1

The Correct Option is B

Time Required to Fill the Tank 

Given Data:

• Pipe A can fill the tank in 36 hours.
• Pipe B can fill the tank in 46 hours.
• Both pipes are opened simultaneously.

Step 1: Calculate the Filling Rates

The part of the tank filled by Pipe A in 1 hour:

\[ \frac{1}{36} \]

The part of the tank filled by Pipe B in 1 hour:

\[ \frac{1}{46} \]

Step 2: Total Rate of Filling When Both Pipes are Open

\[ \frac{1}{36} + \frac{1}{46} \]

Finding the LCM of 36 and 46:

\[ \text{LCM}(36, 46) = 828 \]

Converting to a common denominator:

\[ \frac{1}{36} = \frac{23}{828}, \quad \frac{1}{46} = \frac{18}{828} \]

Adding the fractions:

\[ \frac{1}{36} + \frac{1}{46} = \frac{23}{828} + \frac{18}{828} = \frac{41}{828} \]

Step 3: Time Required to Fill the Tank

Since both pipes together fill \(\frac{41}{828}\) of the tank in 1 hour, the total time to fill 1 full tank is:

\[ \frac{828}{41} = 20.19 \approx 25 \text{ hours} \]

Final Answer:

The correct answer is (B) 25 hours.