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There are 8 filling pipes each capable of filling a cistern alone in 26 minutes and 6 emptying pipes each capable of emptying a cistern alone in 24 minutes. All pipes are opened together and as a result, tank fills 27 litres of water per minute. Find the capacity of the tank.
- a)445 L
- b)458 L
- c)460 L
- d)468 L
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
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There are 8 filling pipes each capable of filling a cistern alone in 2...
one minute work for all pipes together
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There are 8 filling pipes each capable of filling a cistern alone in 2...
one minute work for all pipes together
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There are 8 filling pipes each capable of filling a cistern alone in 2...
Given:
- 8 filling pipes can fill the tank alone in 26 minutes.
- 6 emptying pipes can empty the tank alone in 24 minutes.
- All pipes are opened together and the tank fills at a rate of 27 litres per minute.
To find:
- The capacity of the tank.
Solution:
- Let the capacity of the tank be "C" litres.
- Let the efficiency of each filling pipe be "F" (i.e., each pipe can fill 1/26th of the tank in 1 minute).
- Let the efficiency of each emptying pipe be "E" (i.e., each pipe can empty 1/24th of the tank in 1 minute).
- The net efficiency of all pipes opened together is: (8F - 6E) cisterns per minute (since there are 8 filling pipes and 6 emptying pipes).
- Since the tank fills at a rate of 27 litres per minute, we have: (8F - 6E)C = 27.
- We need to find the value of "C".
To find the values of "F" and "E":
- Since 8 filling pipes can fill the tank alone in 26 minutes, we have: 8F = 1/26 (i.e., each pipe can fill 1/208th of the tank in 1 minute).
- Since 6 emptying pipes can empty the tank alone in 24 minutes, we have: 6E = 1/24 (i.e., each pipe can empty 1/144th of the tank in 1 minute).
- Therefore, F = 1/208 and E = 1/144.
Substituting the values of "F" and "E" in the net efficiency equation, we get:
- (8/208 - 6/144)C = 27
- Simplifying, we get: C = 468.
Therefore, the capacity of the tank is 468 litres.
Answer: Option (D).
- 8 filling pipes can fill the tank alone in 26 minutes.
- 6 emptying pipes can empty the tank alone in 24 minutes.
- All pipes are opened together and the tank fills at a rate of 27 litres per minute.
To find:
- The capacity of the tank.
Solution:
- Let the capacity of the tank be "C" litres.
- Let the efficiency of each filling pipe be "F" (i.e., each pipe can fill 1/26th of the tank in 1 minute).
- Let the efficiency of each emptying pipe be "E" (i.e., each pipe can empty 1/24th of the tank in 1 minute).
- The net efficiency of all pipes opened together is: (8F - 6E) cisterns per minute (since there are 8 filling pipes and 6 emptying pipes).
- Since the tank fills at a rate of 27 litres per minute, we have: (8F - 6E)C = 27.
- We need to find the value of "C".
To find the values of "F" and "E":
- Since 8 filling pipes can fill the tank alone in 26 minutes, we have: 8F = 1/26 (i.e., each pipe can fill 1/208th of the tank in 1 minute).
- Since 6 emptying pipes can empty the tank alone in 24 minutes, we have: 6E = 1/24 (i.e., each pipe can empty 1/144th of the tank in 1 minute).
- Therefore, F = 1/208 and E = 1/144.
Substituting the values of "F" and "E" in the net efficiency equation, we get:
- (8/208 - 6/144)C = 27
- Simplifying, we get: C = 468.
Therefore, the capacity of the tank is 468 litres.
Answer: Option (D).
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