Abhishek can do a piece of work in 40 days. He alone worked at it for 8 days and then Bacchhan completed alone the rest work in 24 days. In how many days they will complete the whole work, working together?

Options

A. `17 1/7` days
B. `18 1/7` days
C. `9 1/6` days
D. 14 days

Answer

To solve the problem, we will follow these steps:

### Step 1: Determine Abhishek's Work Rate
Abhishek can complete the work in 40 days. Therefore, his work rate per day is:
\[ \text{Work Rate of Abhishek} = \frac{1}{40} \text{ (work per day)} \]

### Step 2: Calculate the Work Done by Abhishek in 8 Days
In 8 days, the amount of work done by Abhishek is:
\[ \text{Work Done by Abhishek} = 8 \times \frac{1}{40} = \frac{8}{40} = \frac{1}{5} \]

### Step 3: Determine the Remaining Work
The total work can be considered as 1 unit. After Abhishek's contribution, the remaining work is:
\[ \text{Remaining Work} = 1 - \frac{1}{5} = \frac{4}{5} \]

### Step 4: Calculate Bacchhan's Work Rate
Bacchhan completed the remaining work in 24 days. Therefore, his work rate per day is:
\[ \text{Work Rate of Bacchhan} = \frac{4/5}{24} = \frac{4}{120} = \frac{1}{30} \text{ (work per day)} \]

### Step 5: Calculate Combined Work Rate of Abhishek and Bacchhan
Now, we can find their combined work rate:
\[ \text{Combined Work Rate} = \text{Work Rate of Abhishek} + \text{Work Rate of Bacchhan} = \frac{1}{40} + \frac{1}{30} \]

To add these fractions, we need a common denominator. The least common multiple of 40 and 30 is 120.
\[ \frac{1}{40} = \frac{3}{120}, \quad \frac{1}{30} = \frac{4}{120} \]
Thus,
\[ \text{Combined Work Rate} = \frac{3}{120} + \frac{4}{120} = \frac{7}{120} \]

### Step 6: Calculate the Time Taken to Complete the Whole Work Together
The time taken to complete the whole work together is the reciprocal of their combined work rate:
\[ \text{Time} = \frac{1}{\text{Combined Work Rate}} = \frac{1}{\frac{7}{120}} = \frac{120}{7} \approx 17.14 \text{ days} \]

### Conclusion
Abhishek and Bacchhan, working together, will complete the whole work in approximately 17.14 days.

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