Question:

Three taps A, B and C can fill a tank in 12, 15 and 20 hours respectively. If tap A is open all the time and tap B and tap C are open for one hour each alternately, the tank will be filled in

Show Hint

For problems involving multiple taps, work out the rate of filling for each tap and combine the rates of all taps accordingly.
Updated On: Mar 9, 2025
  • 7 hours
  • 6 hours
  • 5 hours
  • None of these
Hide Solution
collegedunia
Verified By Collegedunia

The Correct Option is A

Solution and Explanation

Let the total capacity of the tank be 1 unit (i.e., the tank is completely filled when the total capacity is reached).
Rate of filling:
- Tap A fills the tank in 12 hours, so the rate of tap A is \( \frac{1}{12} \) of the tank per hour.
- Tap B fills the tank in 15 hours, so the rate of tap B is \( \frac{1}{15} \) of the tank per hour.
- Tap C fills the tank in 20 hours, so the rate of tap C is \( \frac{1}{20} \) of the tank per hour. Filling pattern:
- Tap A is open all the time.
- Tap B and Tap C are opened alternately for 1 hour each.
In 2 hours:
- In the first hour, tap A and tap B are open. The amount of water filled is: \[ \text{Water filled in 1st hour} = \frac{1}{12} + \frac{1}{15} = \frac{5}{60} + \frac{4}{60} = \frac{9}{60} = \frac{3}{20} \] - In the second hour, tap A and tap C are open. The amount of water filled is: \[ \text{Water filled in 2nd hour} = \frac{1}{12} + \frac{1}{20} = \frac{5}{60} + \frac{3}{60} = \frac{8}{60} = \frac{2}{15} \] So, in 2 hours, the total water filled is: \[ \frac{3}{20} + \frac{2}{15} = \frac{9}{60} + \frac{8}{60} = \frac{17}{60} \] Total time to fill the tank: Now, we need to calculate how many such 2-hour cycles are needed to fill the tank. Let’s calculate how many cycles are needed to fill the tank. The total amount of water filled after \( x \) cycles is: \[ \frac{17}{60} \times x = 1 \] Solving for \( x \): \[ x = \frac{60}{17} \approx 3.53 \quad \text{(approximately 3 full cycles and part of the 4th cycle)} \] Since each cycle takes 2 hours, the total time taken to fill the tank is approximately: \[ 2 \times 3.53 = 7.06 \, \text{hours} \] So, the tank will be filled in approximately 7 hours. Thus, the correct answer is (1) 7 hours.
Was this answer helpful?
0
0

Questions Asked in MAT exam

View More Questions