A,B and C together can finish a job in 4 days .A and B together can finish the same job in 5 days .In how many days ,C alone will finish the same job ?

Options

A. 12
B. 16
C. 20
D. 24

Answer

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

### Step 1: Understand the Work Done by A, B, and C
Given:
- A, B, and C together can finish a job in 4 days.
- A and B together can finish the same job in 5 days.

### Step 2: Calculate the Total Work
Let's assume the total work is represented in terms of units. The LCM of 4 days and 5 days is 20. This means we can consider the total work to be 20 units.

### Step 3: Calculate the Work Done by A, B, and C Together
If A, B, and C can finish the job in 4 days, then their combined work rate is:
\[ \text{Work rate of A, B, and C} = \frac{20 \text{ units}}{4 \text{ days}} = 5 \text{ units per day} \]

### Step 4: Calculate the Work Done by A and B Together
If A and B can finish the job in 5 days, then their combined work rate is:
\[ \text{Work rate of A and B} = \frac{20 \text{ units}}{5 \text{ days}} = 4 \text{ units per day} \]

### Step 5: Find the Work Rate of C
Now, we can find the work rate of C by subtracting the work rate of A and B from the work rate of A, B, and C:
\[ \text{Work rate of C} = \text{Work rate of A, B, and C} - \text{Work rate of A and B} \]
\[ \text{Work rate of C} = 5 \text{ units per day} - 4 \text{ units per day} = 1 \text{ unit per day} \]

### Step 6: Calculate the Time Taken by C Alone
To find out how many days C alone will take to finish the job, we can use the formula:
\[ \text{Time taken by C} = \frac{\text{Total Work}}{\text{Work rate of C}} = \frac{20 \text{ units}}{1 \text{ unit per day}} = 20 \text{ days} \]

### Conclusion
C alone will finish the job in **20 days**.

---