To find out how many days Reena alone can complete the work, we first need to understand the work rates for Reena and Jaya combined, and for Jaya alone.
- Step 1: Determine the combined work rate of Reena and Jaya. Reena and Jaya together can complete the work in 6 days. Therefore, their combined work rate is \(\frac{1}{6}\)of the work per day.
- Step 2: Calculate the work rate of Jaya alone. Jaya alone can complete the work in 8 days, so her work rate is \(\frac{1}{8}\)of the work per day.
- Step 3: Establish the equation for Reena's work rate. Let the work rate of Reena alone be \(R\). Thus, the combined work rate can be expressed as: \(R + \frac{1}{8} = \frac{1}{6}\).
- Step 4: Solve for Reena's work rate:
- Subtract Jaya’s work rate from the combined rate: \(R = \frac{1}{6} - \frac{1}{8}\)
- Find a common denominator to subtract the fractions: \(R = \frac{4}{24} - \frac{3}{24} = \frac{1}{24}\)
- Step 5: Interpret the result. Since Reena’s work rate is \(\frac{1}{24}\)of the work per day, Reena can complete the entire work alone in 24 days.
Thus, the correct option is 24 days.
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