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1. A large tanker can be filled by two pipes A and B in 60 minutes and 40 minutes respectively. How many minutes will it take to fill the tanker from empty state if B is used for half the time and A and B fill it together for the other half?

A. 15 minutes

B. 20 minutes

C. 27.5 minutes

D. 30 minutes

Solution:

\begin{aligned} Part filled by (A + B) in 1 minute \\ = \frac{1}{60} + \frac{1}{40} = \frac{1}{24} \\ Suppose the tank is filled in x minutes \\ Then, \frac{x}{2} (\frac{1}{24} + \frac{1}{40}) = 1 \\ \Rightarrow \frac{x}{2} \times \frac{1}{15} = 1 \\ \Rightarrow x = 30 minutes \end{aligned}

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