Raghav can do a piece of work in 15 days while Dev can do the same piece of work in 20 days. If they work together for 4 days, how much fraction of work left?

Options

A. `7//15`
B. `1//2`
C. `8//13`
D. `8//15`

Answer

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

### Step 1: Determine the total work
Raghav can complete the work in 15 days, and Dev can complete it in 20 days. To find the total work, we can use the Least Common Multiple (LCM) of their working days.

- LCM of 15 and 20 = 60

Thus, we can consider the total work as 60 units.

### Step 2: Calculate the work done by Raghav and Dev per day
Next, we need to find the work done by each person in one day.

- Raghav's work per day = Total work / Days taken by Raghav = 60 / 15 = 4 units
- Dev's work per day = Total work / Days taken by Dev = 60 / 20 = 3 units

### Step 3: Calculate the combined work done in one day
Now, we can find the total work done when both Raghav and Dev work together in one day.

- Combined work per day = Raghav's work + Dev's work = 4 + 3 = 7 units

### Step 4: Calculate the total work done in 4 days
Now we calculate how much work they can complete together in 4 days.

- Work done in 4 days = Combined work per day × Number of days = 7 × 4 = 28 units

### Step 5: Calculate the remaining work
Now, we subtract the work done from the total work to find out how much work is left.

- Remaining work = Total work - Work done in 4 days = 60 - 28 = 32 units

### Step 6: Calculate the fraction of work left
Finally, we need to express the remaining work as a fraction of the total work.

- Fraction of work left = Remaining work / Total work = 32 / 60

To simplify this fraction:

- 32 / 60 = 8 / 15

Thus, the fraction of work left is **8/15**.

### Conclusion
The fraction of work left after Raghav and Dev work together for 4 days is **8/15**.

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