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Question
Sita can finish typing a 100 page document in 9 hours. Mita in 6 hours and Rita in 12 hours. How long will they take to type a 100 page document if they work together?
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Solution
\[\text{ Time taken by Sita to do the work = 9 hours } \]
\[\text{ Time taken by Mita to do the work = 6 hours } \]
\[\text{ Time taken by Rita to do the work = 12 hours } \]
\[\text{ Now, } \]
\[\text{ Work done by Sita } = \frac{1}{9}\]
\[\text{ Work done by Mita } = \frac{1}{6}\]
\[\text{ Work done by Rita } = \frac{1}{12}\]
\[ \therefore \text{ Work done by them together } = \frac{1}{9} + \frac{1}{6} + \frac{1}{12}\]
\[ = \frac{4 + 6 + 3}{36} = \frac{13}{36}\]
\[\text{ Thus, together they can do the work in } \frac{36}{13} \text{ hours } .\]
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