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Two pipes A and B can fill a cistern in 37*1/2 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if' the B is turned off after _______ min
- a)14
- b)9
- c)11
- d)2
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Two pipes A and B can fill a cistern in 37*1/2 minutes and 45 minutes ...
Let B be turned off after x minutes. Then
Part filled by (A+B) in x mm. + part filled by A in (30 -x) mm. = 1
Part filled by (A+B) in x mm. + part filled by A in (30 -x) mm. = 1
Most Upvoted Answer
Two pipes A and B can fill a cistern in 37*1/2 minutes and 45 minutes ...
To solve this problem, we need to determine the rate at which each pipe can fill the cistern. We can then use this information to find out how long it would take to fill the cistern if only one pipe is open for a certain amount of time.
Let's assume that pipe A can fill the cistern at a rate of x cisterns per minute, and pipe B can fill the cistern at a rate of y cisterns per minute.
We are given that pipe A and pipe B can fill the cistern in 37.5 minutes and 45 minutes respectively. This means that in 1 minute, pipe A can fill 1/37.5 = 1/37.5 cisterns, and pipe B can fill 1/45 cisterns.
We are also given that both pipes are opened and the cistern is filled in just half an hour, which is 30 minutes. This means that in 30 minutes, both pipes together fill 1 cistern.
Using this information, we can set up the following equation:
(1/37.5)x + (1/45)y = 1
Simplifying this equation, we get:
45x + 37.5y = 37.5*45
Now, we need to find out how long it would take to fill the cistern if only pipe A is open for a certain amount of time. Let's say pipe B is turned off after t minutes.
In t minutes, pipe A can fill t/x cisterns. Since both pipes together fill 1 cistern in 30 minutes, pipe B can fill (30 - t)/45 cisterns in the remaining time.
Setting up the equation and simplifying, we get:
t/x + (30 - t)/45 = 1
Multiplying through by 45x, we get:
45t + 30x - tx = 45x
Simplifying further, we get:
45t = 15x
Dividing both sides by 15x, we get:
t = 3x
This tells us that t must be a multiple of 3x. From the given options, only option B (9 minutes) is a multiple of 3. Therefore, the correct answer is option B.
Let's assume that pipe A can fill the cistern at a rate of x cisterns per minute, and pipe B can fill the cistern at a rate of y cisterns per minute.
We are given that pipe A and pipe B can fill the cistern in 37.5 minutes and 45 minutes respectively. This means that in 1 minute, pipe A can fill 1/37.5 = 1/37.5 cisterns, and pipe B can fill 1/45 cisterns.
We are also given that both pipes are opened and the cistern is filled in just half an hour, which is 30 minutes. This means that in 30 minutes, both pipes together fill 1 cistern.
Using this information, we can set up the following equation:
(1/37.5)x + (1/45)y = 1
Simplifying this equation, we get:
45x + 37.5y = 37.5*45
Now, we need to find out how long it would take to fill the cistern if only pipe A is open for a certain amount of time. Let's say pipe B is turned off after t minutes.
In t minutes, pipe A can fill t/x cisterns. Since both pipes together fill 1 cistern in 30 minutes, pipe B can fill (30 - t)/45 cisterns in the remaining time.
Setting up the equation and simplifying, we get:
t/x + (30 - t)/45 = 1
Multiplying through by 45x, we get:
45t + 30x - tx = 45x
Simplifying further, we get:
45t = 15x
Dividing both sides by 15x, we get:
t = 3x
This tells us that t must be a multiple of 3x. From the given options, only option B (9 minutes) is a multiple of 3. Therefore, the correct answer is option B.
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Two pipes A and B can fill a cistern in 37*1/2 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if' the B is turned off after _______mina)14b)9c)11d)2Correct answer is option 'B'. Can you explain this answer?
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