A's 1 day work: 110
B's 1 day work: \frac{1}{20}
Step 1: A and B work for 4 days:
Work done = 4 \times \left( \frac{1}{10} + \frac{1}{20} \right) = 4 \times \frac{3}{20} = \frac{3}{5}
Remaining work: 1 - \frac{3}{5} = \frac{2}{5}
Step 2: A and C do remaining work in 2 days:
2 \times \left( \frac{1}{10} + \frac{1}{C} \right) = \frac{2}{5}
Dividing both sides by 2:
\frac{1}{10} + \frac{1}{C} = \frac{1}{5}
\frac{1}{C} = \frac{1}{5} - \frac{1}{10} = \frac{1}{10}
\Rightarrow C = 10
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