A can do a work in 10 days, B can do the same work in 20 days. After working for 4 days B left the job & C started working at the place of B, the remaining work was done by both A & C in 2 days. In how many days C alone can do the work?

Work and Time – Find Days for C

A's 1 day work: \( \frac{1}{10} \)
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:
\( \frac{1}{10} + \frac{1}{C} = \frac{1}{5} \)

\( \frac{1}{C} = \frac{1}{5} - \frac{1}{10} = \frac{1}{10} \)
\( \Rightarrow C = 10 \)

✅ Final Answer: 10 days