The question in the image reads:

Q59: Three workers, A, B, and C, can complete a task in 6, 9, and 12 days respectively, when working alone. They started working together for 2 days, and then A stops working. How many additional days will it take for B and C to complete the remaining work together?

Options: A. 5.36
B. 3.26
C. 2.86
D. 1.43

Let’s calculate the solution:

1. Individual work rates (per day):

   • A's rate = $\frac{1}{6}$ of the task/day.
   • B's rate = $\frac{1}{9}$ of the task/day.
   • C's rate = $\frac{1}{12}$ of the task/day.

2. Combined work rate for A, B, and C: $\text{Total rate} = \frac{1}{6} + \frac{1}{9} + \frac{1}{12}$ To compute this, we find the least common denominator (LCD = 36): $\text{Total rate} = \frac{6}{36} + \frac{4}{36} + \frac{3}{36} = \frac{13}{36}$

   Hence, together, A, B, and C complete $\frac{13}{36}$ of the task in one day.

3. Work done in 2 days: $\text{Work done in 2 days} = 2 \times \frac{13}{36} = \frac{26}{36} = \frac{13}{18}$

   So, $\frac{13}{18}$ of the task is completed in 2 days, leaving: $\text{Remaining work} = 1 - \frac{13}{18} = \frac{5}{18}$

4. Combined work rate for B and C: $\text{Rate of B and C} = \frac{1}{9} + \frac{1}{12}$ LCD = 36: $\text{Rate of B and C} = \frac{4}{36} + \frac{3}{36} = \frac{7}{36}$

5. Time taken to complete remaining work: $\text{Time} = \frac{\text{Remaining work}}{\text{Rate of B and C}} = \frac{\frac{5}{18}}{\frac{7}{36}} = \frac{5}{18} \times \frac{36}{7} = \frac{10}{7} \approx 1.43 \, \text{days.}$

Answer: D. 1.43

Let me know if you'd like a detailed breakdown of any step!

Related Questions:

1. How do you calculate the total work rate when multiple workers are involved?
2. How can you estimate time taken for tasks using proportions?
3. What happens if another worker joins midway? How does it impact calculations?
4. How do you determine the fraction of work completed at a specific time?
5. How do varying work efficiencies affect collaboration outcomes?

Tip:

When solving work-rate problems, always calculate the combined rate first and handle remaining tasks step by step!