10 men can complete a piece of work in 15 days and 15 women can complete the same work in 12 days. If all the 10 men and 15 women work together, in how many days will the work get completed?

Options

A. 6
B. `6 (1)/(3)`
C. `6 (2)/(3)`
D. `7 (2)/(3)`

Answer

To solve the problem step by step, we will first determine the work done by the men and women individually, and then combine their efforts to find out how long it will take them to complete the work together.

### Step 1: Determine the total work in terms of units.
Given that 10 men can complete the work in 15 days, we can calculate the total work in units.

- Total work = Number of men × Days × Work done per day by each man.
- Let's assume the total work is 60 units (as derived from the LCM approach in the video).

### Step 2: Calculate the work done by 10 men in one day.
- Work done by 10 men in 15 days = 60 units.
- Therefore, work done by 10 men in 1 day = Total work / Days = 60 units / 15 days = 4 units.

### Step 3: Calculate the work done by 15 women in one day.
Given that 15 women can complete the same work in 12 days:

- Work done by 15 women in 12 days = 60 units.
- Therefore, work done by 15 women in 1 day = Total work / Days = 60 units / 12 days = 5 units.

### Step 4: Calculate the combined work done by 10 men and 15 women in one day.
- Combined work done in one day = Work done by 10 men + Work done by 15 women = 4 units + 5 units = 9 units.

### Step 5: Calculate the total number of days required to complete the work together.
- Total work = 60 units.
- Work done in one day = 9 units.
- Therefore, number of days required = Total work / Work done in one day = 60 units / 9 units = 6.67 days, which can be expressed as 6 complete 2/3 days.

### Final Answer:
The work will be completed in **6 complete 2/3 days**.

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