Discussion
Pipe A can fill a tank 5 times faster than Pipe B and takes 32 minutes less than Pipe B to fill the tank. If both the pipes are opened together, then in how much time the tank would be full?
Answer: C
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).
A is five times as fast, so A's time is a fifth of B's.
\[ B - \frac{B}{5} = 32 \quad\Longrightarrow\quad \frac{4B}{5} = 32 \]
\[ B = 40, \qquad A = 8 \text{ minutes} \]
\[ \frac{1}{8} + \frac{1}{40} = \frac{5 + 1}{40} = \frac{3}{20} \]
\[ t = \frac{20}{3} \text{ minutes} \]
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