Sabir is thrice as good as Anish in work. Sabir is able to finish a job in 60 days less than Anish. Both can finish the work in - days working together.

Options

A. 18 days
B. `22 (1)/2 days `
C. 24 days
D. 26 days

Answer

To solve the problem step by step, let's denote:

- The number of days Anish takes to complete the work as \( D \).
- Since Sabir is thrice as good as Anish, his efficiency can be represented as \( 3 \) times Anish's efficiency.

### Step 1: Establish the relationship between Sabir's and Anish's work days
Given that Sabir finishes the job in 60 days less than Anish, we can express this as:
\[ D_S = D - 60 \]
where \( D_S \) is the number of days Sabir takes to complete the work.

### Step 2: Relate their efficiencies to the number of days
Since efficiency is inversely proportional to the number of days taken to complete the work, we can write:
- Efficiency of Anish = \( \frac{1}{D} \)
- Efficiency of Sabir = \( \frac{1}{D - 60} \)

Given that Sabir is thrice as efficient as Anish, we can express this as:
\[ \frac{1}{D - 60} = 3 \cdot \frac{1}{D} \]

### Step 3: Set up the equation
Cross-multiplying gives us:
\[ D = 3(D - 60) \]
Expanding this:
\[ D = 3D - 180 \]
Rearranging the equation:
\[ 180 = 3D - D \]
\[ 180 = 2D \]
\[ D = 90 \]

### Step 4: Calculate Sabir's days
Now that we have \( D \), we can find the number of days Sabir takes:
\[ D_S = D - 60 = 90 - 60 = 30 \]

### Step 5: Calculate the total work done
The total work can be calculated using the efficiency:
- Total work = Efficiency × Days
- For Anish: \( \text{Total Work} = \frac{1}{90} \times 90 = 1 \) (1 unit of work)
- For Sabir: \( \text{Total Work} = \frac{1}{30} \times 30 = 1 \) (1 unit of work)

### Step 6: Calculate the combined work rate
When working together, their combined efficiency is:
\[ \text{Combined Efficiency} = \frac{1}{D} + \frac{1}{D_S} = \frac{1}{90} + \frac{1}{30} \]
Finding a common denominator (which is 90):
\[ \text{Combined Efficiency} = \frac{1}{90} + \frac{3}{90} = \frac{4}{90} = \frac{2}{45} \]

### Step 7: Calculate the time taken when working together
If their combined efficiency is \( \frac{2}{45} \), the time taken to complete the work together is:
\[ \text{Time} = \frac{\text{Total Work}}{\text{Combined Efficiency}} = \frac{1}{\frac{2}{45}} = \frac{45}{2} = 22.5 \text{ days} \]

### Conclusion
Thus, both Sabir and Anish can finish the work together in \( 22.5 \) days.