Ram and Shyam work on a job together for four days and complete 60% of it. Ram takes leave then and Shyam works for eight more days to complete the job. How long would Ram take to complete the entire job alone?

Correct Option

The problem requires determining the individual time Ram takes to complete the entire job. This can be calculated by first establishing the combined and individual work rates.

• Ram and Shyam together complete 60% of the job in 4 days. Their combined one-day work rate is $\frac{60}{100}\times \frac{1}{4}=\frac{3}{20}$ of the job.
• The remaining 40% of the job is completed by Shyam alone in 8 days. Therefore, Shyam's one-day work rate is $\frac{40}{100}\times \frac{1}{8}=\frac{1}{20}$ of the job.
• If Shyam completes $\frac{1}{20}$ of the job in one day, he would take 20 days to complete the entire job alone.
• Let Ram's one-day work rate be $\frac{1}{x}$ and Shyam's one-day work rate be $\frac{1}{y}$. From the above, we know $\frac{1}{y}=\frac{1}{20}$.
• The combined one-day work rate is $\frac{1}{x}+\frac{1}{y}=\frac{3}{20}$.
• Substituting Shyam's rate into the combined rate equation: $\frac{1}{x}+\frac{1}{20}=\frac{3}{20}$.
• Solving for $\frac{1}{x}$: $\frac{1}{x}=\frac{3}{20}-\frac{1}{20}=\frac{2}{20}=\frac{1}{10}$.
• Therefore, Ram's one-day work rate is $\frac{1}{10}$ of the job, which implies Ram would take 10 days to complete the entire job alone.

Incorrect Options

Options 1 (6 days), 2 (8 days), and 4 (11 days) are incorrect as the calculated time for Ram to complete the entire job alone is 10 days.