K alone can complete a work in 20 days and M alone can complete the same work in 30 days. K and M start the work together but K leaves the work after 5 days of the starting of work. In how many days M will complete the remaining work?

Options

A. `35/2` days
B. `25/2` days
C. `55/2` days
D. `45/2` days

Answer

To solve the problem, we will follow these steps:

### Step 1: Determine the work done by K and M in one day.
- K can complete the work in 20 days, so K's work in one day = 1/20 of the work.
- M can complete the work in 30 days, so M's work in one day = 1/30 of the work.

### Step 2: Calculate the combined work done by K and M in one day.
- Combined work done by K and M in one day = (1/20 + 1/30).
- To add these fractions, we need a common denominator. The LCM of 20 and 30 is 60.
- K's work in one day = 3/60 and M's work in one day = 2/60.
- Therefore, combined work = (3/60 + 2/60) = 5/60 = 1/12 of the work.

### Step 3: Calculate the work done by K and M together in the first 5 days.
- Work done in 5 days = 5 * (1/12) = 5/12 of the work.

### Step 4: Determine the remaining work after 5 days.
- Total work = 1 (whole work).
- Remaining work = 1 - 5/12 = 7/12 of the work.

### Step 5: Calculate how long it will take M to complete the remaining work.
- M's work in one day = 1/30 of the work.
- To find the time taken by M to complete the remaining work (7/12), we use the formula:
\[ \text{Time} = \frac{\text{Remaining work}}{\text{M's work in one day}} = \frac{7/12}{1/30} \]
- This simplifies to:
\[ \text{Time} = \frac{7}{12} \times 30 = \frac{210}{12} = 17.5 \text{ days} \]

### Final Answer:
M will complete the remaining work in **17.5 days**.

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