Discussion
A cistern has two taps attached to it. Tap B can empty the cistern in 45 minutes. But Tap A can fill the cistern in just 30 minutes. Rohit started both taps unknowingly but realized his mistake after 30 minutes. He immediately closed Tap B. Now after this, in how much time will the cistern be filled?
Answer: D
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).
For the first 30 minutes both taps run:
\[ \frac{1}{30} - \frac{1}{45} = \frac{3 - 2}{90} = \frac{1}{90} \text{ per minute} \]
\[ 30 \times \frac{1}{90} = \frac{1}{3} \text{ filled} \]
With Tap B closed, the remaining \( \tfrac{2}{3} \) is filled at \( \tfrac{1}{30} \) per minute:
\[ \frac{2}{3} \times 30 = 20 \text{ minutes} \]
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