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Two pipes A and B can fill a tank in 20 hours and 24 hours respectively, if the two pipes opened at 5 am in the morning, then at what time the pipe A should be closed to completely fill the tank exactly at 5 in the evening?
  • a)
    3 pm
  • b)
    2 pm
  • c)
    4 pm
  • d)
    1 pm
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Two pipes A and B can fill a tank in 20 hours and 24 hours respectivel...
Two pipes A and B can fill a tank in 20 hours and 24 hours respectively,
Let total work be 120 units,
As B worked for all the time,
⇒ Work done by B in 12 hours = 120/24 × 12 = 60 units
Remaining work was done by A,
⇒ A would take 60 × 20/120 hours = 10 hours
∴ A should be closed at 3 pm.
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Most Upvoted Answer
Two pipes A and B can fill a tank in 20 hours and 24 hours respectivel...
To solve this problem, we need to find the time it takes for pipe A to fill the tank and then subtract that time from the total time available (from 5 am to 5 pm) to determine when pipe A should be closed.

Let's calculate the time it takes for pipe A to fill the tank:

- Pipe A can fill the tank in 20 hours.
- Therefore, in 1 hour, pipe A can fill 1/20th of the tank.

Now let's calculate the time it takes for pipe B to fill the tank:

- Pipe B can fill the tank in 24 hours.
- Therefore, in 1 hour, pipe B can fill 1/24th of the tank.

Since both pipes are open from 5 am to 5 pm, we have a total of 12 hours available to fill the tank. Now we can calculate the amount of the tank filled by each pipe in 12 hours:

- Pipe A can fill (1/20) x 12 = 12/20 = 3/5 of the tank in 12 hours.
- Pipe B can fill (1/24) x 12 = 12/24 = 1/2 of the tank in 12 hours.

Since we want to completely fill the tank, the sum of the amounts filled by both pipes should be equal to 1.

- (3/5) + (1/2) = 6/10 + 5/10 = 11/10

Therefore, the combined fill rate of both pipes is greater than 1. This means that pipe A alone can fill the tank in less than 12 hours.

To find the exact time when pipe A should be closed, we need to calculate the time it takes for pipe A to fill the tank completely:

- Pipe A can fill 1/20th of the tank in 1 hour.
- Therefore, pipe A can fill the entire tank in 20 hours.

Since pipe A needs to be closed at 5 pm, we need to subtract 20 hours from the total time available (12 hours):

- 12 - 20 = -8

As the result is negative, it means that pipe A should be closed 8 hours before 5 pm, which is 9 am.

Therefore, pipe A should be closed at 9 am in order to completely fill the tank by 5 pm.
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