Neena, Meena and Tina can do a piece of work in 4 days, 8 days and 6 days respectively. Neena and Tina work together for 1 day and then Neena leaves and Tina is joined by Meena to complete the work. How long does Tina work(in hours)?

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Solution

Work done by Neena in 1 day $\to \frac{W}{4}$

Work done by Meena in 1 day $\to \frac{W}{8}$

Work done by Tina in 1 day $\to \frac{W}{6}$

Now, work done in 1 day by Neena and Tina $\to \frac{W}{4} + \frac{W}{6} = \frac{5 W}{12}$

Then Neena Leaves and tina is joined by Meena

$\frac{5 W}{12} + x (\frac{W}{8} + \frac{W}{6}) = W \Rightarrow \frac{5}{12} + x (\frac{7}{24}) = 1 \Rightarrow x (\frac{7}{24}) = 1 - \frac{5}{12} \Rightarrow x (\frac{7}{24}) = \frac{7}{12} \Rightarrow x = 2 d a y s$

Hence, tina Works for $2 + 1 = 3$ days

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