Tap M and N can together fill a cistern in 48/13 minutes. N alone can fill it in 6 minutes. How much time will M alone take to fill the cistern?

Correct option is D

Let Tap M fill the cistern alone in m minutes and Tap N fill it alone in n minutes.
Given n = 6. The part of the cistern each tap fills per minute is 1/m for M, and 1/6 for N. When operating together, their combined rate is 1/m + 1/6. We know they fill the cistern in 48/13 minutes together, so
1/m + 1/6 = 1/((48/13)) = 13/48
Hence,
1/m = 13/48 - 1/6 = 13/48 - 8/48 = 5/48
Therefore, m = 48/5 = 9.6 minutes.