MAT Exam 2020 Paper

Concept:The filling rate minus the leak rate gives the slower net filling rate.Explanation:Normal filling time is $6$ hours.So, the normal fill rate is $\frac{1}{6}$ cistern per hour.Due to the leak, it takes $6+4=10$ hours to fill.So, the net fill rate with the leak is $\frac{1}{10}$ cistern per hour.Let the leak alone empty the full cistern in $t$ hours.Then, the leak rate is $\frac{1}{t}$ cistern per hour.Thus,$$\frac{1}{6}-\frac{1}{t}=\frac{1}{10}$$$$\Rightarrow \frac{1}{t}=\frac{1}{6}-\frac{1}{10}=\frac{5-3}{30}=\frac{2}{30}=\frac{1}{15}$$Hence, $t=15$ hours.Answer:The leak will empty the full cistern in $15$ hours. (Option B)