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Pipes A and B can fill a cistern in 15 hours together. But if these pipes operate separately A takes 40 hours less than B to fill the tank. In how many hours the pipe A will fill the cistern working alone?
- a)60
- b)20
- c)40
- d)15
- e)25
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Pipes A and B can fill a cistern in 15 hours together. But if these pi...
Let A takes x hours, then B = (x+40) hours
1/x + 1/(x+40) = 1/15
Solve, x = 20
1/x + 1/(x+40) = 1/15
Solve, x = 20
Most Upvoted Answer
Pipes A and B can fill a cistern in 15 hours together. But if these pi...
Let A takes x hours, then B = (x+40) hours
1/x + 1/(x+40) = 1/15
Solve, x = 20
1/x + 1/(x+40) = 1/15
Solve, x = 20
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Community Answer
Pipes A and B can fill a cistern in 15 hours together. But if these pi...
Given:
Pipes A and B can fill a cistern in 15 hours together.
A takes 40 hours less than B to fill the tank when operated separately.
To find:
In how many hours the pipe A will fill the cistern working alone?
Solution:
Let the capacity of the cistern be C.
Let the rate of filling of pipe A be x.
Then, the rate of filling of pipe B will be x - (C/40) [as A takes 40 hours less than B to fill the tank]
Using the formula: Time = (Capacity/Rate)
Time taken by A to fill the cistern = C/x
Time taken by B to fill the cistern = C/(x - C/40)
Together, A and B can fill the cistern in 15 hours.
Using the formula: Time = (Capacity/Rate)
15 = C/x + C/(x - C/40)
Multiplying both sides by x(x - C/40), we get:
15x(x - C/40) = C(x - C/40) + Cx
15x^2 - 15Cx/40 = 2Cx - C^2/40
600x^2 - 15Cx = 80Cx - C^2
600x^2 - 95Cx + C^2 = 0
Solving this quadratic equation, we get:
x = C/20 or x = C/30
Since x cannot be greater than (x - C/40), the rate of filling of A will be x = C/30.
Therefore, the time taken by pipe A to fill the cistern alone = C/x = 30 hours.
Hence, option (b) 20 is incorrect, the correct answer is option (a) 60.
Pipes A and B can fill a cistern in 15 hours together.
A takes 40 hours less than B to fill the tank when operated separately.
To find:
In how many hours the pipe A will fill the cistern working alone?
Solution:
Let the capacity of the cistern be C.
Let the rate of filling of pipe A be x.
Then, the rate of filling of pipe B will be x - (C/40) [as A takes 40 hours less than B to fill the tank]
Using the formula: Time = (Capacity/Rate)
Time taken by A to fill the cistern = C/x
Time taken by B to fill the cistern = C/(x - C/40)
Together, A and B can fill the cistern in 15 hours.
Using the formula: Time = (Capacity/Rate)
15 = C/x + C/(x - C/40)
Multiplying both sides by x(x - C/40), we get:
15x(x - C/40) = C(x - C/40) + Cx
15x^2 - 15Cx/40 = 2Cx - C^2/40
600x^2 - 15Cx = 80Cx - C^2
600x^2 - 95Cx + C^2 = 0
Solving this quadratic equation, we get:
x = C/20 or x = C/30
Since x cannot be greater than (x - C/40), the rate of filling of A will be x = C/30.
Therefore, the time taken by pipe A to fill the cistern alone = C/x = 30 hours.
Hence, option (b) 20 is incorrect, the correct answer is option (a) 60.
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