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Tap A can fill a tank in 9 hours and tap B can fill the same tank in 6 hours. Tap C can empty the same full tank in 4 hours. If all the taps are opened together, then what portion of the tank will be filled after 6 hours?
- a)1/5
- b)1/15
- c)1/6
- d)1/18
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Tap A can fill a tank in 9 hours and tap B can fill the same tank in 6...
A can fill the tank in = 9 hours
∴ In 1 hour A can fill = 1/9
B can fill the tank in = 6 hours
∴ In 1 hour B can fill = 1/6
C can empty the tank in = 4 hours
∴ In 1 hour C can empty = 1/4
∴ In 6 hours they together can fill ,
Most Upvoted Answer
Tap A can fill a tank in 9 hours and tap B can fill the same tank in 6...
Understanding the Problem
To solve how much of the tank will be filled after 6 hours with taps A, B, and C working together, we first need to determine the rate at which each tap works.
Rates of Taps
- Tap A: Fills the tank in 9 hours.
- Rate = 1/9 tank per hour
- Tap B: Fills the tank in 6 hours.
- Rate = 1/6 tank per hour
- Tap C: Empties the tank in 4 hours.
- Rate = -1/4 tank per hour (negative because it empties)
Combined Rate
Now, we add the rates of all three taps:
- Combined Rate = Rate of A + Rate of B - Rate of C
- Combined Rate = (1/9 + 1/6 - 1/4)
To combine these fractions, we first find a common denominator, which is 36.
- (1/9 = 4/36)
- (1/6 = 6/36)
- (1/4 = 9/36)
So, we have:
- Combined Rate = (4/36 + 6/36 - 9/36) = (4 + 6 - 9) / 36 = 1/36 tank per hour
Calculating Total Filled in 6 Hours
Now, we calculate how much of the tank is filled in 6 hours:
- Amount filled in 6 hours = Combined Rate × Time
- Amount filled = (1/36) × 6 = 6/36 = 1/6
Conclusion
After 6 hours, the portion of the tank that will be filled is 1/6.
Therefore, the correct answer is option 'C'.
To solve how much of the tank will be filled after 6 hours with taps A, B, and C working together, we first need to determine the rate at which each tap works.
Rates of Taps
- Tap A: Fills the tank in 9 hours.
- Rate = 1/9 tank per hour
- Tap B: Fills the tank in 6 hours.
- Rate = 1/6 tank per hour
- Tap C: Empties the tank in 4 hours.
- Rate = -1/4 tank per hour (negative because it empties)
Combined Rate
Now, we add the rates of all three taps:
- Combined Rate = Rate of A + Rate of B - Rate of C
- Combined Rate = (1/9 + 1/6 - 1/4)
To combine these fractions, we first find a common denominator, which is 36.
- (1/9 = 4/36)
- (1/6 = 6/36)
- (1/4 = 9/36)
So, we have:
- Combined Rate = (4/36 + 6/36 - 9/36) = (4 + 6 - 9) / 36 = 1/36 tank per hour
Calculating Total Filled in 6 Hours
Now, we calculate how much of the tank is filled in 6 hours:
- Amount filled in 6 hours = Combined Rate × Time
- Amount filled = (1/36) × 6 = 6/36 = 1/6
Conclusion
After 6 hours, the portion of the tank that will be filled is 1/6.
Therefore, the correct answer is option 'C'.
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Tap A can fill a tank in 9 hours and tap B can fill the same tank in 6 hours. Tap C can empty the same full tank in 4 hours. If all the taps are opened together, then what portion of the tank will be filled after 6 hours?a)1/5b)1/15c)1/6d)1/18Correct answer is option 'C'. Can you explain this answer?
Question Description
Tap A can fill a tank in 9 hours and tap B can fill the same tank in 6 hours. Tap C can empty the same full tank in 4 hours. If all the taps are opened together, then what portion of the tank will be filled after 6 hours?a)1/5b)1/15c)1/6d)1/18Correct answer is option 'C'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about Tap A can fill a tank in 9 hours and tap B can fill the same tank in 6 hours. Tap C can empty the same full tank in 4 hours. If all the taps are opened together, then what portion of the tank will be filled after 6 hours?a)1/5b)1/15c)1/6d)1/18Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Tap A can fill a tank in 9 hours and tap B can fill the same tank in 6 hours. Tap C can empty the same full tank in 4 hours. If all the taps are opened together, then what portion of the tank will be filled after 6 hours?a)1/5b)1/15c)1/6d)1/18Correct answer is option 'C'. Can you explain this answer?.
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