Two pipes A and B can fill a cistern in 4 hrs. Had they been opened separately, then B would have taken 6 hrs more than A to fill the cistern. How much time will be taken by A to fill the cistern separately?
Solution
Correct Answer: Option C
Let the cistern be filled by pipe A alone in ‘x’ hours.
Then, pipe B will fill it in (x+6) hrs. Now, according to the question:
\(\eqalign{ & \Rightarrow \frac{1}{x} + \frac{1}{{\left( {x + 6} \right)}} = \frac{1}{4} \cr & \Rightarrow \frac{{x + 6 + x}}{{x\left( {x + 6} \right)\;}} = \frac{1}{4} \cr & \Rightarrow {x^2} - 2x - 24 = 0 \cr & \Rightarrow (x - 6)(x + 4) = 0 \cr & \Rightarrow x = 6 \cr}\)
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