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1. A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the tank completely?

A. 3 hrs 15 min

B. 3 hrs 45 min

C. 4 hrs

D. 4 hrs 15 min

Solution:

Time taken by one tap to fill half of the the tank = 3 hours
Part filled by the four taps in 1 hour

\begin{aligned} = 4 \times \frac{1}{6} = \frac{2}{3} \\ Remaining part = 1 - \frac{1}{2} = \frac{1}{2} \\ ∴ \frac{2}{3} : \frac{1}{2} :: 1 : x \\ \Rightarrow x = \frac{1}{2} \times 1 \times \frac{3}{2} \\ = \frac{3}{4} h r s . i . e ., 45 mins . \\ So, total time taken = 3 h r s . 45 m i n s . \end{aligned}

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