Question

There are two tanks A and B to fill up a water tank. The tank can be filled in 40 min together by A and B, if the tank can be filled in 60 min when tap A alone is on. How much time will tap B alone take to fill up the tank?

• A. 64 min
• B. 80 min
• C. 96 min
• D. 120 min

Hint:

To find individual rates from combined work rates, use addition of rates and solve for unknown.

Answer 1

The Correct Option is D

Step 1: Define rates
- Tap A fills in 60 min → rate of A = \(\frac{1}{60}\) tank/min
- Tap B fills in \(x\) min → rate of B = \(\frac{1}{x}\) tank/min
Step 2: Combined rate
Together they fill in 40 min → combined rate = \(\frac{1}{40}\) tank/min
Step 3: Set up equation
\[ \frac{1}{60} + \frac{1}{x} = \frac{1}{40} \] Step 4: Solve for \(x\)
\[ \frac{1}{x} = \frac{1}{40} - \frac{1}{60} = \frac{3 - 2}{120} = \frac{1}{120} \] \[ x = 120 \] Thus, Option (D) 120 min is correct.