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Pipe A can fill the tank in 4 hours, while pipe B can fill it in 6 hours working separately. Pipe C can empty the whole tank in 4 hours. Ramesh opened the pipe A and B simultaneously to fill the empty tank. He wanted to adjust his alarm so that he could open the pipe C when it was half-filled, but he mistakenly adjusted his alarm at a time when his tank would be 3/4th filled. What is the time difference between both the cases, to fill the tank fully.
  • a)
    48 min.
  • b)
    54 min.
  • c)
    30 min.
  • d)
    None of these
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Pipe A can fill the tank in 4 hours, while pipe B can fill it in 6 hou...
In ideal case :
Time taken to fill the half tank by A and B = 50 / 41.66 = 6 / 5 hours
Time taken by A,B and C to fill rest half of the tank = 50 / 16.66 = 3 hours
Total time = 
In second case :
Time taken to fill 3 / 4 tank by A and B = 75 / 41.66 = 9 / 5 hours
Time taken by A,B and C to fill rest 1 / 4 tank = 25 / 16.66 = 3 / 2 hours
Total time = 9 / 5 + 3 / 2 = 3 hours 18 minutes
Therefore, difference in time = 54 minutes
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Most Upvoted Answer
Pipe A can fill the tank in 4 hours, while pipe B can fill it in 6 hou...
Given information:

- Pipe A can fill the tank in 4 hours
- Pipe B can fill the tank in 6 hours
- Pipe C can empty the tank in 4 hours
- Ramesh opened pipe A and B simultaneously to fill the empty tank.

Approach:

- Let the capacity of the tank be x.
- Let t be the time taken to fill the tank when pipes A and B work together.
- Use the formula, Work = Rate x Time, to form equations for the rates of each pipe.
- Use the equation, Work = Capacity, to form an equation for the work done when the tank is 3/4th filled.
- Solve the equations to find the value of t and the time difference between both the cases.

Solution:

- Let the capacity of the tank be x.
- Let t be the time taken to fill the tank when pipes A and B work together.
- Rate of pipe A = x/4 per hour
- Rate of pipe B = x/6 per hour
- Rate of pipe C = -x/4 per hour (negative sign indicates emptying of the tank)
- Work done by pipes A and B in time t = (x/4 + x/6) t = (5x/12) t
- Work done by pipe C in time t = -(x/4) t
- Work done when the tank is 3/4th filled = (3/4) x
- Equating the work done by pipes A, B and C to fill the tank to the work done when the tank is 3/4th filled, we get:
- (5x/12) t - (x/4) t = (3/4) x
- Solving for t, we get t = 36 minutes
- To find the time taken to fill the tank fully, we need to subtract the time taken to fill the tank up to 3/4th from the time taken to fill the tank fully.
- Time taken to fill the remaining 1/4th of the tank = (1/4) x / (x/4 + x/6) = 54 minutes
- Therefore, the time difference between both the cases is 54 - 36 = 18 minutes = 54/3 minutes.
- Hence, the correct answer is option (b).

Therefore, the time difference between both the cases is 54 - 36 = 18 minutes = 54/3 minutes.
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Community Answer
Pipe A can fill the tank in 4 hours, while pipe B can fill it in 6 hou...
Pipe A can fill the tank in 4 hours, while pipe B can fill it in 6 hours working separately. Pipe C can empty the whole tank in 4 hours. Ramesh opened the pipe A and B simultaneously to fill the empty tank. He wanted to adjust his alarm so that he could open the pipe C when it was half-filled, but he mistakenly adjusted his alarm at a time when his tank would be 3/4th filled. What is the time difference between both the cases, to fill the tank fully.

A:  48 min.

B:  54 min.

C:  30 min.

D:  None of these
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Pipe A can fill the tank in 4 hours, while pipe B can fill it in 6 hours working separately. Pipe C can empty the whole tank in 4 hours. Ramesh opened the pipe A and B simultaneously to fill the empty tank. He wanted to adjust his alarm so that he could open the pipe C when it was half-filled, but he mistakenly adjusted his alarm at a time when his tank would be 3/4th filled. What is the time difference between both the cases, to fill the tank fully.a)48 min.b)54 min.c)30 min.d)None of theseCorrect answer is option 'B'. Can you explain this answer?
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