Pipe A and B running together can fill a cistern in 6 minutes. If Pipe

Let the capacity of the tank be x litres (which is the work to be done). The question says that pipes A and B can fill the cistern in 6 minutes, when working together. Therefore, combined rate of A and B = \(\frac{x}{6}\) litres per minute.

Remember that for questions on Time and Work, the fundamental equation is Work = Time * Rate. When you know two of the variables, it's not hard to find the third.

If A can fill the cistern in 'a' minutes, B can fill it in (a+5) minutes. So,

Rate of pipe A = \(\frac{x}{a}\) litres per minute and Rate of pipe B = \(\frac{x}{(a+5)}\) litres per minute. Substituting this in the equation representing the combined rate of A and B, we have,

\(\frac{x}{a}\) + \(\frac{x}{(a+5)}\) = \(\frac{x}{6}\).

The LCM of the denominators is a(a+6). Simplifying the equation above, we have,

\(\frac{(2a + 5)}{ a(a+5)}\) = \(\frac{1}{6}\) which yields the values of a as 10 and -3 respectively. Since 'a' represents the time taken for pipe A to do the work, we discard the negative value and keep a=10.

This means, pipe A can fill the cistern in 10 minutes. There is only one option like that and that is option E.
The correct answer option is E.

Hope that helps!