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?

3 hrs 15 min

3 hrs 45 min

4 hrs

4 hrs 15 min

Explanation:

Time taken by one tap to fill half of the tank = 3 hrs.

Part filled by the four taps in 1 hour =$ \left(4 \times\dfrac{1}{6} \right) $=$ \dfrac{2}{3} $.

Remaining part =$ \left(1 -\dfrac{1}{2} \right) $=$ \dfrac{1}{2} $.

$\therefore \dfrac{2}{3} $:$ \dfrac{1}{2} $:: 1 : $ x $

$\Rightarrow x $ =$ \left(\dfrac{1}{2} \times 1 \times\dfrac{3}{2} \right) $=$ \dfrac{3}{4} $hours i.e., 45 mins.

So, total time taken = 3 hrs. 45 mins.