Anil can do a work in 10 days and Babu in 8 days. Anil and Babu can do the work on alternate days. If Anil begins the work, then the work can be finished in how many days?

Options

A. 9 days
B. 12 days
C. 7 days
D. 8 days

Answer

To solve the problem step by step, we will first determine how much work Anil and Babu can complete in a day, then calculate the total work done over a period of days, and finally find out how many days it takes to complete the work.

### Step 1: Determine the total work
Anil can complete the work in 10 days, and Babu can complete it in 8 days. To find a common measure of work, we can take the Least Common Multiple (LCM) of their working days.

- LCM of 10 and 8 = 40

So, we will consider the total work as 40 units.

### Step 2: Calculate work done per day
Now, we need to find out how much work Anil and Babu can do in one day.

- Work done by Anil in one day = Total work / Days taken by Anil = 40 / 10 = 4 units
- Work done by Babu in one day = Total work / Days taken by Babu = 40 / 8 = 5 units

### Step 3: Work done in two days
Since Anil and Babu work on alternate days, we can calculate the total work done in a 2-day cycle.

- Day 1: Anil works and completes 4 units.
- Day 2: Babu works and completes 5 units.

Total work done in 2 days = Work done by Anil + Work done by Babu = 4 + 5 = 9 units.

### Step 4: Calculate total cycles needed
Now, we need to find out how many such 2-day cycles are needed to complete the total work of 40 units.

- Total work = 40 units
- Work done in 2 days = 9 units

Number of complete 2-day cycles = Total work / Work done in 2 days = 40 / 9 ≈ 4.44 cycles.

Since we can only complete whole cycles, we will complete 4 full cycles.

### Step 5: Calculate work done in 4 cycles
In 4 cycles (which is 8 days), the total work done will be:

- Total work done in 4 cycles = 4 cycles * 9 units = 36 units.

### Step 6: Calculate remaining work
After 8 days, the total work done is 36 units. Therefore, the remaining work is:

- Remaining work = Total work - Work done = 40 - 36 = 4 units.

### Step 7: Determine who will work next
Since Anil starts the work, he will work on the 9th day.

On the 9th day, Anil will work and complete 4 units of work.

### Step 8: Conclusion
Thus, the total time taken to finish the work is:

- Total days = 8 days (from the 4 cycles) + 1 day (Anil's work on the 9th day) = 9 days.

Therefore, Anil and Babu can finish the work in **9 days**.

---