A does `(7)/(10)` part of work in 15 days. After that he completes the remaining work in 4 days with the help of B. In how many days will A and B together do the same work?

Options

A. `10(1)/(3)` days
B. `12(2)/(3)` days
C. `13(1)/(3)` days
D. `8(1)/(4)` days

Answer

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

### Step 1: Determine the work done by A in 15 days
A does \( \frac{7}{10} \) of the work in 15 days.

### Step 2: Calculate the remaining work
The total work is considered as 1. Therefore, the remaining work after A has completed \( \frac{7}{10} \) is:
\[ \text{Remaining work} = 1 - \frac{7}{10} = \frac{3}{10} \]

### Step 3: Determine the time taken to complete the remaining work with B
A and B together complete the remaining \( \frac{3}{10} \) of the work in 4 days.

### Step 4: Calculate the work done by A and B together in one day
To find out how much work A and B can do together in one day, we can use the formula:
\[ \text{Work done by A and B in 1 day} = \frac{\text{Total work}}{\text{Time taken}} = \frac{\frac{3}{10}}{4} = \frac{3}{40} \]

### Step 5: Calculate the time taken by A and B to complete the entire work
Now, to find out how many days A and B together will take to complete the entire work (1 unit of work), we can use the formula:
\[ \text{Time taken} = \frac{\text{Total work}}{\text{Work done in 1 day}} = \frac{1}{\frac{3}{40}} = \frac{40}{3} \text{ days} \]

### Step 6: Convert the time into mixed fraction
To convert \( \frac{40}{3} \) into a mixed fraction:
\[ \frac{40}{3} = 13 \frac{1}{3} \text{ days} \]

### Final Answer
Thus, A and B together will complete the work in \( 13 \frac{1}{3} \) days.

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