A cistern can be filled by two pipes. The small pipe alone will take 24 minutes longer than the larger pipe to fill the cistern alone. The small pipe alone will take 32 minutes longer to fill the cistern alone than when two pipes are operating together. How long will it take the larger pipe to fill the cistern alone?

Assign variables to the time it takes for the cistern to be filled by each pipe.

Let the time the small pipe takes be 's'
Let the time the large pipe takes be 'l'

1. s - 24 = l
(For them to be equal, you have to remove 24 min from the time the smaller pipe takes)

2. Here, the time T the two pipes take is given by \frac1T = \frac1s + \frac1l. (When both are used, the time decreases, so you cannot add s and l directly. This is from a concept of 'shared work')

That gives T = \frac{sl}{s+l}

Now the second equation will be s - 32 = \frac{sl}{s+l}

Since you need to find 'l' alone make 's' the subject of the formula in the first equation. Then, substitute 's' by the expression in 'l' in the second equation. Solve for 'l' to have your answer.

Feel free to ask if you still have difficulties :)