Three people A, B, and C are assigned work. The table below shows the actual work done by A and B and the maximum time taken by each to complete their work:

| People | Actual Work Done (Units) | Maximum Time Taken (Hours) |
|--------|--------------------------|----------------------------|
| A | 50 | 10 |
| B | 60 | 12 |
| C | ? | 15 |

If C works in cycles of 1 hour working followed by 15 minutes rest, repeating this pattern until the total 15 hours are completed, and C's efficiency is 20% more than the average of the minimum efficiencies of A and B, find the total work done by C (in units).

Question

Three people A, B, and C are assigned work. The table below shows the actual work done by A and B and the maximum time taken by each to complete their work:

| People | Actual Work Done (Units) | Maximum Time Taken (Hours) |
|--------|--------------------------|----------------------------|
| A      | 50                       | 10                         |
| B      | 60                       | 12                         |
| C      | ?                        | 15                         |

If C works in cycles of 1 hour working followed by 15 minutes rest, repeating this pattern until the total 15 hours are completed, and C's efficiency is 20% more than the average of the minimum efficiencies of A and B, find the total work done by C (in units).

Accepted Answer

**Solution:**

1. Calculate the efficiency of A and B:
   - Efficiency = Work done / Time taken
   - Efficiency of A = $ $\frac{50}{10} = 5$ $ units/hour
   - Efficiency of B = $ $\frac{60}{12} = 5 $$ units/hour

2. Minimum efficiency between A and B is 5 units/hour.

3. Average of minimum efficiency of A and B is simply 5 (since both are equal).

4. Efficiency of C is 20% more than this average:
   - Efficiency of C = 5 + 20\%$ \times $5 = 5 + 1 = 6 units/hour

5. C works in cycles of 1 hour work + 15 minutes rest = 1.25 hours per cycle.

6. Total time available for C is 15 hours.

7. Number of complete cycles C can work:
   - Number of cycles = $ $\frac{15}{1.25} = 12$ $ cycles

8. Total working hours of C = 12 cycles $ $\times 1$ $ hour = 12 hours

9. Total work done by C = Efficiency $ $\times $$ Total working hours = 6 $ $\times$ $ 12 = 72 units

**Answer:** 72 units

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