Discussion
Pipe R can empty a full tank in 30 hours. But two pipes P and Q can fill a tank in 15 hours and 10 hours respectively. Ram unknowingly opened all three taps. After 2 hours Shyam realized it and closed Pipe R. Due to this mistake how much time more would it take to fill the tank?
Answer: B
Work in rates: a pipe that fills a tank in \( n \) units of time fills \( \tfrac{1}{n} \) of it per unit, and rates add (an emptying pipe counting negative).
With all three open:
\[ \frac{1}{15} + \frac{1}{10} - \frac{1}{30} = \frac{2 + 3 - 1}{30} = \frac{2}{15} \text{ per hour} \]
\[ 2 \text{ hours} \rightarrow \frac{4}{15} \text{ filled} \]
After R is closed, P and Q fill at \( \tfrac{1}{15} + \tfrac{1}{10} = \tfrac{1}{6} \):
\[ \frac{11}{15} \div \frac{1}{6} = 4.4 \text{ hours} \]
\[ \text{total} = 2 + 4.4 = 6.4 \text{ h}, \qquad \text{without the mistake} = 6 \text{ h} \]
\[ \text{extra} = 0.4 \text{ h} = 24 \text{ minutes} \]
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