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Question
A cistern can be filled by one tap in 8 hours, and by another in 4 hours. How long will it take to fill the cistern if both taps are opened together?
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Solution
\[\text{ Time taken by the first tap to fill the cistern = 8 hours } \]
\[\text{ Time taken by the second tap to fill the cistern = 4 hours } \]
\[ \therefore \text{ Work done by the first tap in 1 hour } = \frac{1}{8}\]
\[ \text{ Work done by the second tap in 1 hour } = \frac{1}{4}\]
\[ \therefore \text{ Work done by both the taps in 1 hour } = \frac{1}{8} + \frac{1}{4}\]
\[ = \frac{1 + 2}{8} = \frac{3}{8}\]
\[\text{ Thus, both the taps together will fill the cistern in } \frac{8}{3} \text{ hours or } 2\frac{2}{3} \text{ hours } .\]
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