A and B can together finish a work in 30 days. They worked together for 20 days and then B left. After another 20 days. A finished the remaining work. In how many days A alone can finish the job?

Options

A. 50 days
B. 60 days
C. 48 days
D. 54 days

Answer

To solve the problem, we will follow these steps:

### Step 1: Determine the work done by A and B together in one day.
Since A and B can finish the work together in 30 days, the amount of work they complete in one day is:
\[ \text{Work done by A and B in one day} = \frac{1}{30} \]

### Step 2: Calculate the work done by A and B in 20 days.
In 20 days, the work done by A and B together is:
\[ \text{Work done in 20 days} = 20 \times \frac{1}{30} = \frac{20}{30} = \frac{2}{3} \]

### Step 3: Determine the remaining work after 20 days.
The total work is considered as 1 (or 100%). After A and B have worked together for 20 days, the remaining work is:
\[ \text{Remaining work} = 1 - \frac{2}{3} = \frac{1}{3} \]

### Step 4: Calculate the work done by A in the next 20 days.
After B leaves, A finishes the remaining work in 20 days. Therefore, the rate at which A works can be calculated as follows:
Let \( A \)'s work rate be \( a \) (work done by A in one day). In 20 days, A completes the remaining work of \( \frac{1}{3} \):
\[ 20a = \frac{1}{3} \]
From this, we can solve for \( a \):
\[ a = \frac{1}{3} \div 20 = \frac{1}{60} \]

### Step 5: Determine how long A alone would take to finish the job.
Since A can complete \( \frac{1}{60} \) of the work in one day, the total time taken by A to finish the entire work (1 unit of work) is:
\[ \text{Time taken by A alone} = \frac{1}{a} = \frac{1}{\frac{1}{60}} = 60 \text{ days} \]

### Final Answer:
A alone can finish the job in **60 days**.

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