Question

30 women can complete a work in 20 days. After how many days should the number of women be increased by 40% so as to complete work in 75% of time

Answer 1

30 women can complete a work in 20 days. It means that the work requires the input of 30x20 = 600 woman-days. The work needs to be completed in 75% time, that is, in 15 days. And the women force is to be increased by 40% that is by 12 women.

Let 30 women work for x days and (30+12 = 42) women work for (15-x) days. Hence the equation is

30x + 42(15-x) = 600, or

30x + 630 - 42x = 600, or

-12x = -30, or

x = 30/12 = 2.5 days.

Check: 30 women working for 2.5 days and 42 women working for 12.5 days = 30*2.5 + 42*12.5 = 75 + 525 = 600 woman days.

Answer: 30 women work for 2.5 days and 42 women work for 12.5 days to complete the work in 15 days.