A alone can complete a work in 12 days, and B alone can complete the same work in 30 days. A and B work together for 6 days, after which C replaces both. If C completes 50% of the remaining work, what percentage of the total work is done by C?

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**Solution:**

1. Calculate the daily work rate of A and B:
   - A's one day work = $\frac{1}{12}$
   - B's one day work = $\frac{1}{30}$

2. Work done by A and B together in one day:
   $$\frac{1}{12} + \frac{1}{30} = \frac{5}{60} + \frac{2}{60} = \frac{7}{60}$$

3. Work done by A and B in 6 days:
   $$6 	imes \frac{7}{60} = \frac{42}{60} = \frac{7}{10} = 70\%$$

4. Remaining work after 6 days:
   $$100\% - 70\% = 30\%$$

5. C completes 50% of the remaining work:
   $$50\% 	imes 30\% = 15\%$$

6. Therefore, C has done 15% of the total work.

**Answer:** 15\%

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