Three workers, working all days can do a work in 10 days, but one of them having other employment can work only half time. In how many days the work can be finished.

Options

A. 15 days
B. 16 days
C. 12 days
D. `12.5` days

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the Total Work
Let’s denote the total work required to complete the task as \( x \). According to the problem, 3 workers can complete the work in 10 days.

### Step 2: Calculate Work Done by One Worker
If 3 workers can complete the work in 10 days, then the amount of work done by 1 worker in 1 day can be calculated as follows:
\[ \text{Work done by 1 worker in 1 day} = \frac{x}{3 \times 10} = \frac{x}{30} \]

### Step 3: Adjust for the Worker Who Works Half Time
Since one of the workers can only work half time, we need to adjust the work done by this worker. The two full-time workers will do:
\[ \text{Work done by 2 workers in 1 day} = 2 \times \frac{x}{30} = \frac{2x}{30} = \frac{x}{15} \]
The half-time worker will do:
\[ \text{Work done by half-time worker in 1 day} = \frac{x}{30} \times \frac{1}{2} = \frac{x}{60} \]

### Step 4: Calculate Total Work Done by All Workers in One Day
Now, we can find the total work done by all three workers in one day:
\[ \text{Total work done in 1 day} = \text{Work by 2 full-time workers} + \text{Work by half-time worker} \]
\[ = \frac{x}{15} + \frac{x}{60} \]

### Step 5: Find a Common Denominator
To add these fractions, we need a common denominator. The least common multiple of 15 and 60 is 60. Thus, we can convert:
\[ \frac{x}{15} = \frac{4x}{60} \]
Now we can add:
\[ \text{Total work done in 1 day} = \frac{4x}{60} + \frac{x}{60} = \frac{5x}{60} = \frac{x}{12} \]

### Step 6: Calculate the Number of Days to Complete the Work
If the total work is \( x \) and the work done in one day is \( \frac{x}{12} \), then the total number of days required to complete the work is:
\[ \text{Number of days} = \frac{\text{Total work}}{\text{Work done in one day}} = \frac{x}{\frac{x}{12}} = 12 \text{ days} \]

### Final Answer
Thus, the work can be finished in **12 days**.

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