Question

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

• A. 20
• B. 25
• C. 35
• D. 30
• E.

Hint:

For combined rates of work, add the individual rates to find the total rate. Then, the time taken is the reciprocal of the combined rate.

Answer 1

The Correct Option is B

Step 1: Consider the total work as filling the tank, where the rate of work is measured in terms of "tank filled per hour." - Pipe A fills the entire tank in 36 hours, so its rate of work per hour is: \[ \text{Rate of A} = \frac{1}{36} \] - Pipe B takes 46 hours to fill the tank, meaning its hourly work rate is: \[ \text{Rate of B} = \frac{1}{46} \] Step 2: When both pipes are opened together, their combined work rate is: \[ \frac{1}{36} + \frac{1}{46} \] To add these fractions, we determine the Least Common Multiple (LCM) of 36 and 46. The LCM of 36 and 46 is 414. Expressing both fractions with a denominator of 414: \[ \frac{1}{36} = \frac{23}{414}, \quad \frac{1}{46} = \frac{9}{414} \] Summing the two fractions: \[ \frac{23}{414} + \frac{9}{414} = \frac{32}{414} = \frac{16}{207} \] Step 3: Since the combined work rate per hour is \( \frac{16}{207} \), the total time required to fill the tank is found by taking the reciprocal: \[ \text{Time taken} = \frac{207}{16} = 25.875 \text{ hours} \approx 25 \text{ hours} \] Thus, the tank will be filled in approximately **25 hours**.