**1. ****A alone can do a piece of work in 6 days and B alone can do it in 12 days. In how many days will A and B together do the same work?**

**Solution:** Let total work = 12 units

it means that A 1 day work = 12/6 2 units

and B one day work = 12/12 = 1 unit

[atex]\Rightarrow[/latex] A and B together one day work = 2 + 1 = 3 units

Time taken to finish the job by A and B together = 12/3 = 4 days

**2.** **Rohit can finish a work in 30 days. Rohit and his friend Rohan working together can finish it in 12 days. In how many days can Rohan do it alone?**

Solution: Let total work = lcm (30, 12) = 60 units

Rohit one day work = 60 / 30 = 2 units

Rohit and Rohan 1 day work = 60/12 = 5 units

[latex]\Rightarrow[/latex] Rohan 1 day work = 5 – 2 = 3 units

Time taken to finish the job by Rohan = 60/3 = 20 days

**3. Priyojit works twice as fast as Pritam. If together they finished the work in 12 days, then how much time Pritam take to do the work?**

Solution: Let Pritam 1 day work = x units

then, Priyojit 1 day work = 2x units

[latex]\Rightarrow[/latex] Both Pritam and Priyojit 1 day work = x + 2x = 3x units

[latex]\Rightarrow[/latex] Pritam and Priyojit 12 day work = 36x units

It means that total work = 36x units

Time taken bypritam to complete the work = 36x/x = 36 units

**4. If Ritam take 50% more time than Rohan to do a work and if they together do the work in 18 days then find how much time shall Ritam take to do the work?**

Solution: Let Ritam 1 day work = 2x units

then, Rohan 1 day work = 3x units

[latex]\Rightarrow[/latex] Both Ritam and Rohan 1 day work = 2x + 3x = 5x units

[latex]\Rightarrow[/latex] Ritam and Rohan 18 day work = 90x units

It means that total work = 90x units

Time taken by Ritam to complete the work = 90x/2x = 45 units

**5. 3 men or 5 women can do a work in 12 days. How long will 6 men and 5 women take to do it**

Solution: 5 women = 3 men

Therefore, 6men + 5 women = 6 men + 3 men = 9 men

3 men do the work in 12 days

1 men do the work in (12*3) days

9 men do the work in (12*3)/9 days = 4 days