Two pipes, M and N, can fill a tank in 10 minutes and 15 minutes,

Step 1: Find rates of the pipes

• Pipe M fills the tank in 10 minutes → rate of M = $ \frac{1}{10} $ tank/min

• Pipe N fills the tank in 15 minutes → rate of N = $ \frac{1}{15} $ tank/min

Step 2: Amount filled in first 5 minutes (both pipes open)

Combined rate = $ \frac{1}{10} + \frac{1}{15} = \frac{3 + 2}{30} = \frac{5}{30} = \frac{1}{6} $ tank/min

Amount filled in 5 minutes = $ 5 \times \frac{1}{6} = \frac{5}{6} $ of the tank

Step 3: Remaining tank to fill

Remaining = $ 1 - \frac{5}{6} = \frac{1}{6} $

Only pipe N works now → rate = $ \frac{1}{15} $ tank/min

Time to fill remaining = $ \frac{1/6}{1/15} = \frac{1}{6} \times \frac{15}{1} = 2.5 $ minutes

Step 4: Total time

Total time = $5 + 2.5 = 7.5$ minutes