Question

If 12 men or 15 women can finish a piece of work in 66 days ,how long will 24 men and 3 women take to finish the work

Answer 1

12 men's work = 15 womens work
1mens work =5/4 women's work
24mens work = 30 women's work

15 women can do a work in 66days
So 1 women can do a work in 66*15 days
Then (30+3)33women can do a work in 66*15/33=30days

Answer 2

30 days are needed for 24 men and 3 women for finishing the work.

Solution:

Given that,

Work of 12 men = Work of 15 Women ………. (1)

Therefore, work of 1 men = work of $\left(\frac{15}{12}\right)$ women

And work of 24 men = work of $\left(\frac{15}{12}\right) \times 24$ women = 30 women …….. (2)

Now, according to the question.  

15 women can finish a work = 66days

So 1 women can finish a work =$\frac{66}{15}$ days

Thus, (24 men + 3 women) = (30+3) women = 33women can finish a work

$=66 \times\left(\frac{15}{33}\right)$ days  

= 30days [Since 24 men = 30 women]

Hence, 24 men and 3 women can finish a work = 30 days .