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A tap can fill a tank in one hour. A second tap empty it in 30 minutes. If both the taps operate simultaneously, how much time is needed to empty the tank?
- a)20 minutes
- b)30 minutes
- c)40 minutes
- d)45 minutes
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A tap can fill a tank in one hour. A second tap empty it in 30 minutes...
In one minute 1/60 + 1/30 = 1/20 of the tank will be empty
Most Upvoted Answer
A tap can fill a tank in one hour. A second tap empty it in 30 minutes...
Problem Analysis:
We are given that one tap can fill the tank in one hour and the second tap can empty the tank in 30 minutes. We need to find out how much time is needed to empty the tank when both taps operate simultaneously.
Solution:
To solve this problem, we can use the concept of work done. The work done by the first tap in one hour is 1 tank (as it can fill the tank in one hour), and the work done by the second tap in 30 minutes is also 1 tank (as it can empty the tank in 30 minutes).
Now, let's assume that both taps are operating simultaneously and let's find out how much work is done in a given time.
Step 1: Determine the work done by each tap per minute.
- The first tap can fill the tank in 60 minutes, so the work done per minute by the first tap is 1/60 tank per minute.
- The second tap can empty the tank in 30 minutes, so the work done per minute by the second tap is 1/30 tank per minute.
Step 2: Find out the net work done per minute when both taps are operating simultaneously.
- When both taps operate simultaneously, the net work done per minute is the sum of the work done per minute by each tap.
- Net work done per minute = (1/60) - (1/30) = -1/60 tank per minute
Step 3: Determine the time needed to empty the tank.
- Since the net work done per minute is negative (-1/60), it means that the tank is being emptied.
- The time needed to empty the tank completely is the reciprocal of the net work done per minute.
- Time needed to empty the tank = 1 / (1/60) = 60 minutes
Therefore, when both taps operate simultaneously, it will take 60 minutes to empty the tank.
We are given that one tap can fill the tank in one hour and the second tap can empty the tank in 30 minutes. We need to find out how much time is needed to empty the tank when both taps operate simultaneously.
Solution:
To solve this problem, we can use the concept of work done. The work done by the first tap in one hour is 1 tank (as it can fill the tank in one hour), and the work done by the second tap in 30 minutes is also 1 tank (as it can empty the tank in 30 minutes).
Now, let's assume that both taps are operating simultaneously and let's find out how much work is done in a given time.
Step 1: Determine the work done by each tap per minute.
- The first tap can fill the tank in 60 minutes, so the work done per minute by the first tap is 1/60 tank per minute.
- The second tap can empty the tank in 30 minutes, so the work done per minute by the second tap is 1/30 tank per minute.
Step 2: Find out the net work done per minute when both taps are operating simultaneously.
- When both taps operate simultaneously, the net work done per minute is the sum of the work done per minute by each tap.
- Net work done per minute = (1/60) - (1/30) = -1/60 tank per minute
Step 3: Determine the time needed to empty the tank.
- Since the net work done per minute is negative (-1/60), it means that the tank is being emptied.
- The time needed to empty the tank completely is the reciprocal of the net work done per minute.
- Time needed to empty the tank = 1 / (1/60) = 60 minutes
Therefore, when both taps operate simultaneously, it will take 60 minutes to empty the tank.
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A tap can fill a tank in one hour. A second tap empty it in 30 minutes. If both the taps operate simultaneously, how much time is needed to empty the tank?a)20 minutesb)30 minutesc)40 minutesd)45 minutesCorrect answer is option 'A'. Can you explain this answer?
Question Description
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