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A tap can fill a tank in 12 minutes and another tap can empty the tank in 6 minutes.If the tank is already full and then both the taps are opened the tank will be
- a)Filled in 6 minutes
- b)Emptied in 6 minutes
- c)Filled in 8 minutes
- d)Emptied in 12 minutes
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A tap can fill a tank in 12 minutes and another tap can empty the tank...
1/12 – 1/6 = 1-2/12 = -1/12
Most Upvoted Answer
A tap can fill a tank in 12 minutes and another tap can empty the tank...
Tank Filling and Emptying
To solve this problem, we need to understand the rates at which the taps fill and empty the tank. Let's consider the rates of the taps:
- The first tap can fill the tank in 12 minutes, which means it can fill 1/12th of the tank in 1 minute.
- The second tap can empty the tank in 6 minutes, which means it can empty 1/6th of the tank in 1 minute.
Tank Filling and Emptying Combined
When both taps are opened together, the rates at which they fill and empty the tank add up. So, the effective rate of filling the tank is the difference between the two rates:
Effective filling rate = (Rate of filling - Rate of emptying)
= (1/12 - 1/6)
= -1/12 (in negative because the emptying rate is greater)
This means that when both taps are opened together, the effective rate of filling the tank is -1/12th of the tank per minute. In other words, the tank will be emptied at a rate of 1/12th of its capacity per minute.
Time to Empty the Tank
Since the tank is already full, it will take a certain amount of time for the tank to be completely emptied. Let's denote this time as 't'.
In 't' minutes, the tank will be emptied at a rate of 1/12th of its capacity per minute. Therefore, the equation representing the emptying of the tank is:
1/12 * t = 1 (since the tank is emptied completely)
Simplifying the equation, we get:
t = 12 minutes
Therefore, it will take 12 minutes for the tank to be completely emptied when both taps are opened together.
Conclusion
Hence, the correct answer is option 'D' - the tank will be emptied in 12 minutes when both taps are opened together.
To solve this problem, we need to understand the rates at which the taps fill and empty the tank. Let's consider the rates of the taps:
- The first tap can fill the tank in 12 minutes, which means it can fill 1/12th of the tank in 1 minute.
- The second tap can empty the tank in 6 minutes, which means it can empty 1/6th of the tank in 1 minute.
Tank Filling and Emptying Combined
When both taps are opened together, the rates at which they fill and empty the tank add up. So, the effective rate of filling the tank is the difference between the two rates:
Effective filling rate = (Rate of filling - Rate of emptying)
= (1/12 - 1/6)
= -1/12 (in negative because the emptying rate is greater)
This means that when both taps are opened together, the effective rate of filling the tank is -1/12th of the tank per minute. In other words, the tank will be emptied at a rate of 1/12th of its capacity per minute.
Time to Empty the Tank
Since the tank is already full, it will take a certain amount of time for the tank to be completely emptied. Let's denote this time as 't'.
In 't' minutes, the tank will be emptied at a rate of 1/12th of its capacity per minute. Therefore, the equation representing the emptying of the tank is:
1/12 * t = 1 (since the tank is emptied completely)
Simplifying the equation, we get:
t = 12 minutes
Therefore, it will take 12 minutes for the tank to be completely emptied when both taps are opened together.
Conclusion
Hence, the correct answer is option 'D' - the tank will be emptied in 12 minutes when both taps are opened together.
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A tap can fill a tank in 12 minutes and another tap can empty the tank...
D
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A tap can fill a tank in 12 minutes and another tap can empty the tank in 6 minutes.If the tank is already full and then both the taps are opened the tank will bea)Filled in 6 minutesb)Emptied in 6 minutesc)Filled in 8 minutesd)Emptied in 12 minutese)None of theseCorrect answer is option 'D'. Can you explain this answer?
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A tap can fill a tank in 12 minutes and another tap can empty the tank in 6 minutes.If the tank is already full and then both the taps are opened the tank will bea)Filled in 6 minutesb)Emptied in 6 minutesc)Filled in 8 minutesd)Emptied in 12 minutese)None of theseCorrect answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A tap can fill a tank in 12 minutes and another tap can empty the tank in 6 minutes.If the tank is already full and then both the taps are opened the tank will bea)Filled in 6 minutesb)Emptied in 6 minutesc)Filled in 8 minutesd)Emptied in 12 minutese)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A tap can fill a tank in 12 minutes and another tap can empty the tank in 6 minutes.If the tank is already full and then both the taps are opened the tank will bea)Filled in 6 minutesb)Emptied in 6 minutesc)Filled in 8 minutesd)Emptied in 12 minutese)None of theseCorrect answer is option 'D'. Can you explain this answer?.
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