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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?

Solution

Correct Option: 4

The first tap fills the tank at a rate of 16\frac{1}{6} tanks per hour. After half the tank is filled, it takes 3 hours to fill that half.

Now, with four taps (the original plus three more), the rate becomes 4×16=234 \times \frac{1}{6} = \frac{2}{3} tanks per hour.

To fill the remaining half tank, the time required is 1/22/3=12×32=34\frac{1/2}{2/3} = \frac{1}{2} \times \frac{3}{2} = \frac{3}{4} hours.

Thus, the total time taken to fill the tank completely is 3+34=3.753 + \frac{3}{4} = 3.75 hours.

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