Question
Two pipes A and B together can fill a cistern in 4 hours. Had they been opened separately, then B would have taken 6 hours more than A to fill the cistern. How much time will be taken by A to fill the cistern separately?
Answer: Option C
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Let the cistern be filled by pipe A alone in x hours.
Then, pipe B will fill it in (x + 6) hours.
So, \(\frac{1}{x}+\frac{1}{(x+6)}=\frac{1}{4}\)
\(\frac{x+6+x}{x(x+6)}=\frac{1}{4}\)
x2 - 2x - 24 = 0
(x -6)(x + 4) = 0
x = 6. [neglecting the negative value of x]
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