The correct answer is option (B):
After 15 minutes
Here's how to solve this problem, explaining the reasoning step-by-step:
First, understand the work rate:
* Pipe A fills the cistern in 30 minutes, so it fills 1/30 of the cistern per minute.
* Pipe B fills the cistern in 40 minutes, so it fills 1/40 of the cistern per minute.
Second, consider the combined work:
* Let's say Pipe A is turned off after 'x' minutes.
* Pipe B is open for the entire 20 minutes.
Third, set up an equation representing the filled cistern:
* Work done by A in 'x' minutes: (x/30)
* Work done by B in 20 minutes: (20/40) = 1/2
* Combined work (equal to the full cistern which is represented by the value of 1): (x/30) + (1/2) = 1
Fourth, solve for 'x':
* Subtract 1/2 from both sides: (x/30) = 1/2
* Multiply both sides by 30: x = 15
Therefore, Pipe A must be turned off after 15 minutes to allow the cistern to be filled in a total of 20 minutes.