A tap can fill a tank in 6 hours. After half the tank is filled, three more simi

Question

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?

Options:

A . 3 hrs 15 min

B . 3 hrs 45 min

C . 4 hrs

D . 4 hrs 15 min

Answer: Option B

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

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

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

So, $\frac{2}{3}:\frac{1}{2}::1:x$

x= $\left(\frac{1}{2}\times1\times\frac{3}{2}\right)=\frac{3}{4}$ hours i.e., 45 mins.

So, total time taken = 3 hrs. 45 mins

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