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

Let the total work be 1 unit

3 men can do a work in 12 days

=> Rate at which 3 men do the work = $$\frac{1}{12}$$

=> Rate at which 6 men do the work = $$2 * \frac{1}{12} = \frac{1}{6}$$

Similarly, rate at which 5 women do the work = $$\frac{1}{12}$$

Rate at which 6 men and 5 women finish the work = $$\frac{1}{6} + \frac{1}{12}$$

= $$\frac{1}{4}$$

=> No. of days required by 6 men and 5 women to finish the work = $$\frac{1}{\frac{1}{4}}$$

= 4 days