Question

14 men can do a work in 18 days ,15 women can do a work in 24 days. If 14 men work for first three days and 10 women work after that for three days find the part of work left after that? ​

Answer 1

Answer:

$\frac{3}{4}th part of the work remains$

Explanation:

14 men can do the work in 18 days, therefore

1 men can do the  work in 18$\times$14 days

$\therefore in 1 day 1 man will complete \frac{1}{18\times14} part of the work. \\\\\implies in 1 day 14 men will complete$

$\frac{14}{14\times18} part of the work \\\\\therefore in 3 days they will complete \frac{14\times3}{14\times18}=\frac{1}{6} part of the work$

15 women can do the work in 24 days, therefore

1 woman can do the  work in 24$\times$15 days

$\therefore in 1 day 1 woman will complete \frac{1}{24\times15} part of the work. \\\\\implies in 1 day 10 women will complete$

$\frac{10}{24\times15} part of the work \\\\\therefore in 3 days they will complete \frac{10\times3}{24\times15}=\frac{1}{12} part of the work$

Therefore total work completed by them becomes

$\frac{1}{6} +\frac{1}{12} =\frac{1}{4} \\\\ The remaining work will be 1-\frac{1}{4}=\frac{3}{4}$

Answer 2

Question-

14 men can do a piece of work in 18 days, 15 women can do a piece of work in 24 days. If 14 men work for the first three days and 10 women work after that for three days find the part of work left after that? ​

Answer-

Let us assume that the work done by every man is equal and the work done by every woman is equal.

14 men can do a piece of work = 18 days

14 men's work done in one day = 1/18 of the work

15 women can do a piece of work = 24 days

15 women's work done in one day = 1/24

1 women's work done in one day = 1/(24 × 15)

10 women's work done in one day = 10/(24 × 15)

Work done by 14 men in 3 days = 3/18

                                                     = 1/6 of the work

Work done by 10 women in 2 days = (10 × 3)/(24 × 15)

                                                          = (2)/(24)

                                                          = 1/12 of the work

Total work done = 1/6 + 1/12 = (2 + 1)/12 = 3/12 = 1/4 of the work

Remaining work = 1 - 1/4 = 3/4

3/4 of the total work would be left.