A and C can finish a work in 40 days. They worked at it for 10 days and then A left. The remaining work is done by C alone in 30 more days. How long will it take C to finish the work alone?

Options

A. 30 days
B. 22 days
C. 40 days
D. 25 days

Answer

To solve the problem step by step, let's break it down:

### Step 1: Determine the combined work rate of A and C
A and C can finish the work together in 40 days. This means their combined work rate is:
\[ \text{Work rate of A + C} = \frac{1 \text{ unit of work}}{40 \text{ days}} = \frac{1}{40} \text{ units per day} \]

**Hint:** Remember that the work rate is calculated as the total work done divided by the time taken.

### Step 2: Calculate the work done by A and C in 10 days
In 10 days, A and C will complete:
\[ \text{Work done in 10 days} = \text{Work rate} \times \text{Time} = \frac{1}{40} \times 10 = \frac{10}{40} = \frac{1}{4} \text{ units} \]

**Hint:** Multiply the work rate by the number of days to find the total work completed.

### Step 3: Determine the remaining work
Since they completed \(\frac{1}{4}\) of the work, the remaining work is:
\[ \text{Remaining work} = 1 - \frac{1}{4} = \frac{3}{4} \text{ units} \]

**Hint:** Subtract the completed work from the total work to find out how much is left.

### Step 4: Find out how long C takes to finish the remaining work
C completes the remaining \(\frac{3}{4}\) units of work in 30 days. Therefore, C's work rate can be calculated as:
\[ \text{Work rate of C} = \frac{\text{Work done}}{\text{Time}} = \frac{\frac{3}{4}}{30} = \frac{3}{120} = \frac{1}{40} \text{ units per day} \]

**Hint:** Use the formula for work rate (work done divided by time) to find C's efficiency.

### Step 5: Calculate how long it will take C to finish the work alone
Since C's work rate is \(\frac{1}{40}\) units per day, the time taken by C to complete 1 unit of work is:
\[ \text{Time taken by C} = \frac{1 \text{ unit}}{\frac{1}{40} \text{ units per day}} = 40 \text{ days} \]

**Hint:** To find the time taken for one unit of work, take the reciprocal of the work rate.

### Conclusion
C will take **40 days** to finish the work alone.

**Final Answer:** 40 days

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