Work Rate Calculation
First, determine the daily work rate for both Raghav and Akshay.
- Raghav's daily work rate: $\frac{1}{15}$ of the work.
- Akshay's daily work rate: $\frac{1}{20}$ of the work.
Combined Work Rate
Calculate their combined daily work rate when they work together.
Combined rate = Raghav's rate + Akshay's rate
Combined rate = $\frac{1}{15} + \frac{1}{20}$
To add these fractions, find a common denominator, which is 60.
Combined rate = $\frac{4}{60} + \frac{3}{60} = \frac{7}{60}$ of the work per day.
Work Done in 4 Days
Calculate the total fraction of work they complete together in 4 days.
Work done = Combined rate $\times$ Number of days
Work done = $\frac{7}{60} \times 4$
Work done = $\frac{28}{60}$
Simplify the fraction: Work done = $\frac{7}{15}$
Fraction of Work Left
Determine the fraction of the work that remains unfinished.
Total work is represented as 1.
Work left = Total work - Work done
Work left = $1 - \frac{7}{15}$
Work left = $\frac{15}{15} - \frac{7}{15} = \frac{8}{15}$
Therefore, the fraction of the work left is $\frac{8}{15}$.
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