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Q)

A tap can fill a tank in 6 hours. When the tank is half filled, three more similar taps are opened to fill water into the same tank. What is the total time taken to fill the tank completely by all the four pipes?

Explanation

1 pipe can completely fill the tank in 6 hours

therefore, $\frac{6\mathrm{parts}}{6\mathrm{hours}}=\frac{1\mathrm{part}}{1\mathrm{hour}}$

After first pipe fills 3 parts (half tank), 3 more pipes are added.

Now altogether four pipes are filling the remaining 3 parts (half tank)

3 parts of the tank can be filled in 3 hours (180 min) by each of the pipes

1 pipe -- 3 parts -- 180 min

4 pipes -- 3 parts -- X

$=\frac{1\times 3\times 180}{4\times 3\times \left(\mathrm{x}\right)}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}=\frac{180}{4\mathrm{x}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\therefore \mathrm{x}=\frac{180}{4}=45\mathrm{min}$

So it takes 45 minutes to fill the remaining tank.

Hence total time taken by all the four pipes to fill the tank is,

3 hours by first pipe + 45 min by all four pipes together

Total 3 hours 45 minutes.

**Hence option D is correct.**

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