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A needs 6h for the complete pool, so in 1h A fills 1/6 of the pool
B work rate is 1/4
A+B together have a rate of = 1/6 + 1/4= 10/24= 5/12

Formula = R*T=W . 5/12*X = 1-1/6 units of pool that still needs to be filled up

5/12 * X =5/6 --> X=5/6*12/5 --> X=2 so after A has worked one hour, both together need additional 2 hours. This results in 3hours in total for filling the pool.

Hence, D
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Pipe A in 1 hour will fill \(\frac{1}{6} ^{th}\) part of pool.

The remaining part of \(\frac{5}{6}\) will be filled by both A and B at the together rate of \(\frac{1}{6} + \frac{1}{4} = \frac{5}{12}\)

So, to fill the \(\frac{5}{6}\) part of the pool together at the rate of \(\frac{5}{12}\), both A and B will take 2 hours.

Total time taken : 1 + 2 = 3 hours

Answer D
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