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A water tank of capacity 6000 liters is connected to 2 taps ‘A’ and ‘B’. Water flows from these 2 taps at 90 liters per minute and 60 liters per minute respectively. To fill this empty tank, first tap ‘A’ is opened for some time and once it is closed, tap ‘B’ is opened till the tank is full taking a total of 90 minutes. What is the difference in the time (in minutes) for which the taps are opened to fill the tank?
- a)20
- b)30
- c)70
- d)50
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A water tank of capacity 6000 liters is connected to 2 taps ‘A&r...
Let x and y be the time for which tap ‘A’ and ‘B’ are opened
We have x + y = 90 … (i)
90x + 60y = 6000 … (ii)
Solving (i) and (ii), gives x = 20 and y = 70.
⇒ Difference in the duration for which taps ‘A' and ‘B’ are opened = 70 – 20 = 50 minutes.
Most Upvoted Answer
A water tank of capacity 6000 liters is connected to 2 taps ‘A&r...
Let's assume that the first tap can fill the tank in x hours and the second tap can fill the tank in y hours.
The rate at which the first tap fills the tank is 6000/x liters per hour.
The rate at which the second tap fills the tank is 6000/y liters per hour.
If both taps are open, the combined rate at which they fill the tank is (6000/x) + (6000/y) liters per hour.
We know that the combined rate is equal to the rate at which the tank gets filled in 2 hours, which is 6000/2 = 3000 liters per hour.
Therefore, we can write the equation:
(6000/x) + (6000/y) = 3000
To solve this equation, we can multiply both sides by xy to eliminate the denominators:
6000y + 6000x = 3000xy
Simplifying the equation, we get:
2y + 2x = xy
xy - 2x - 2y = 0
Now, let's factor out the common terms:
x(y - 2) - 2(y - 2) = 0
Factor out (y - 2):
(y - 2)(x - 2) = 0
We have two possible solutions for this equation:
1. y - 2 = 0, which means y = 2
2. x - 2 = 0, which means x = 2
Therefore, one possible solution is x = 2 hours and y = 2 hours, which means both taps take 2 hours to fill the tank.
Note: There may be other possible solutions depending on the values of x and y, but in this case, x = 2 and y = 2 is the only solution that satisfies the given conditions.
The rate at which the first tap fills the tank is 6000/x liters per hour.
The rate at which the second tap fills the tank is 6000/y liters per hour.
If both taps are open, the combined rate at which they fill the tank is (6000/x) + (6000/y) liters per hour.
We know that the combined rate is equal to the rate at which the tank gets filled in 2 hours, which is 6000/2 = 3000 liters per hour.
Therefore, we can write the equation:
(6000/x) + (6000/y) = 3000
To solve this equation, we can multiply both sides by xy to eliminate the denominators:
6000y + 6000x = 3000xy
Simplifying the equation, we get:
2y + 2x = xy
xy - 2x - 2y = 0
Now, let's factor out the common terms:
x(y - 2) - 2(y - 2) = 0
Factor out (y - 2):
(y - 2)(x - 2) = 0
We have two possible solutions for this equation:
1. y - 2 = 0, which means y = 2
2. x - 2 = 0, which means x = 2
Therefore, one possible solution is x = 2 hours and y = 2 hours, which means both taps take 2 hours to fill the tank.
Note: There may be other possible solutions depending on the values of x and y, but in this case, x = 2 and y = 2 is the only solution that satisfies the given conditions.
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A water tank of capacity 6000 liters is connected to 2 taps ‘A’ and ‘B’. Water flows from these 2 taps at 90 liters per minute and 60 liters per minute respectively. To fill this empty tank, first tap ‘A’ is opened for some time and once it is closed, tap ‘B’ is opened till the tank is full taking a total of 90 minutes. What is the difference in the time (in minutes) for which the taps are opened to fill the tank?a)20b)30c)70d)50Correct answer is option 'D'. Can you explain this answer?
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A water tank of capacity 6000 liters is connected to 2 taps ‘A’ and ‘B’. Water flows from these 2 taps at 90 liters per minute and 60 liters per minute respectively. To fill this empty tank, first tap ‘A’ is opened for some time and once it is closed, tap ‘B’ is opened till the tank is full taking a total of 90 minutes. What is the difference in the time (in minutes) for which the taps are opened to fill the tank?a)20b)30c)70d)50Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A water tank of capacity 6000 liters is connected to 2 taps ‘A’ and ‘B’. Water flows from these 2 taps at 90 liters per minute and 60 liters per minute respectively. To fill this empty tank, first tap ‘A’ is opened for some time and once it is closed, tap ‘B’ is opened till the tank is full taking a total of 90 minutes. What is the difference in the time (in minutes) for which the taps are opened to fill the tank?a)20b)30c)70d)50Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A water tank of capacity 6000 liters is connected to 2 taps ‘A’ and ‘B’. Water flows from these 2 taps at 90 liters per minute and 60 liters per minute respectively. To fill this empty tank, first tap ‘A’ is opened for some time and once it is closed, tap ‘B’ is opened till the tank is full taking a total of 90 minutes. What is the difference in the time (in minutes) for which the taps are opened to fill the tank?a)20b)30c)70d)50Correct answer is option 'D'. Can you explain this answer?.
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