Pipes M and N running together can fill a cistern in 6 minutes. If M takes 5 minutes less than N to fill the cistern, then the time in which N alone can fill the cistern will be

Question: Pipes M and N running together can fill a cistern in 6 minutes. If M takes 5 minutes less than N to fill the cistern, then the time in which N alone can fill the cistern will be

Solution:
Let,
Pipe M fills the cistern in x minutes.
Therefore, pipe N will fill the cistern in (x + 5) minutes.

Now,
Or, 1/x + 1/(x+5) = 1/6
Or, (x + 5 + x)/ x(x + 5) = 1/6
Or, (2x + 5)/(x² + 5x) = 1/6
Or, x² + 5x = 12x + 30
Or, x² − 7x − 30 = 0
Or, x² − 10x + 3x -30 = 0
Or, x(x − 10) + 3(x − 10) = 0
Or, (x − 10) (x + 3) = 0
∴ x = 10

Thus, pipe M can fill in 10 minutes
So, N can fill in 10 + 5 = 15 minutes.