A alone can do a work in 12 days and B alone can do the same work in 30 days. A and B work together for six days, and then C replaced both. If C complete the 50% of the remaining work, then find the percentage of the work done by C?

The correct option is 15%.

To find the percentage of the work done by C, we first calculate the amount of work completed by A and B during the 6 days they worked together.

Let the total work be represented as 1 unit.
A alone can complete the work in 12 days, so A's work rate per day is:
$\frac{1}{12}$
B alone can complete the work in 30 days, so B's work rate per day is:
$\frac{1}{30}$

When A and B work together, their combined daily work rate is:
$\text{Combined rate}=\frac{1}{12}+\frac{1}{30}$
Finding a common denominator of 60, we get:
$\text{Combined rate}=\frac{5+2}{60}=\frac{7}{60}$

Since A and B work together for 6 days, the work they complete is:
$\text{Work completed in 6 days}=6\times \frac{7}{60}=\frac{7}{10}$
Converting this fraction into a percentage:
$\frac{7}{10}\times 100\%=70\%$

The remaining work is:
$\text{Remaining work}=100\%-70\%=30\%$

C replaces A and B and completes 50% of this remaining work. The percentage of the total work done by C is:
$\text{Work done by C}=50\%\text{of}30\%$
$\text{Work done by C}=0.50\times 30\%=15\%$

Thus, C completes 15% of the total work.