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Mathematics Problem

Mathematics Problem Solution - 14 January

I want to fill my bucket using both cold and hot water.
I have two taps for both cold and hot water. The hot water tap fills the bucket in exact 6 hours and cold water tap fills the bucket in exact 4 hours.
I turn both of them simultaneously but i forgot to turn off another tap which remove the water out of bucket. This tap can empty the bucket in 12 hours.

How Long will it take to fill the bucket ?

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Solution
3 hours

Explanation :
(1/6 + 1/4 - 1/12) ^ (-1)
= (1/3)^(-1) = 3