Rathin & Bratin together can complete a piece of work in 12 days. They start the work together but Rathin had to leave 7.5 days before the work got over. As a result it took a total of 15 days to complete the work. How many days would it have taken Bratin to complete the work by himself?
(a)20
(b)24
(c)30
(d)28

Options

A. 20
B. 24
C. 30
D. 28

Answer

To solve the problem step by step, we will first determine the work done by Rathin and Bratin together, then find out how much work Bratin completed alone after Rathin left.

### Step 1: Determine the work rate of Rathin and Bratin together
Rathin and Bratin together can complete the work in 12 days. Therefore, their combined work rate is:
\[ \text{Work rate of Rathin and Bratin} = \frac{1}{12} \text{ work per day} \]

### Step 2: Calculate the total work done in 7.5 days
They work together for 7.5 days. The amount of work done by both in that time is:
\[ \text{Work done in 7.5 days} = 7.5 \times \frac{1}{12} = \frac{7.5}{12} = \frac{5}{8} \text{ of the work} \]

### Step 3: Determine the remaining work
Since the total work is considered as 1, the remaining work after 7.5 days is:
\[ \text{Remaining work} = 1 - \frac{5}{8} = \frac{3}{8} \text{ of the work} \]

### Step 4: Calculate the time taken by Bratin to complete the remaining work
Bratin works alone for the remaining time, which is \(15 - 7.5 = 7.5\) days. We know that he completes \(\frac{3}{8}\) of the work in 7.5 days. Therefore, we can find Bratin's work rate:
\[ \text{Bratin's work rate} = \frac{\frac{3}{8}}{7.5} = \frac{3}{8 \times 7.5} = \frac{3}{60} = \frac{1}{20} \text{ work per day} \]

### Step 5: Calculate how long it would take Bratin to complete the entire work alone
If Bratin can do \(\frac{1}{20}\) of the work in one day, then the total time taken by Bratin to complete the work alone is:
\[ \text{Time taken by Bratin} = \frac{1}{\frac{1}{20}} = 20 \text{ days} \]

Thus, the answer is that it would take Bratin **20 days** to complete the work by himself.

### Final Answer
(a) 20