Question

a particular work can be completed by 6 men and 6 women in 24 days whereas the same work can be completed by 8 men and 12 womens in 15 days find the time taken by 4 men and 6 women to complete the same work​

Answer 1

In 24 days wowork can be completed by 6 men and 6 women

in a one day work can be completed by 24 (6+6 woman)

=144 men and 144 women

in 15 days work can be completed by 8 men and 12 women
in a one day work can be completed by 15 (8 men+12woman)=120men+180woman
1: according to amount of work done 144 men + 144 women is equal to 120 men + 180 women
24men =36woman
1man=36/24woman
1man=3/2woman

2:Since 6 Men + 6 women is equal to 6 multiplied 3 over 2 + 6 is equal to 9 + 6 is equal to 15 women
and 4 men+ 6woman=4*3/2+6
=6+6=12woman
given 6 men + 6 women completed work in 24 days
15 women completed work in 24 days
one woman complete work in is equal to 24 multiply 15
12 women complete work in =24*15/12=30days
so 4 men and 6 women complete work in 30 days

Answer 2

Given,

6men + 6 women = 24 days

⇒ 6M + 6W = 24

and, 8M + 12W =15

1)Applying, M×D = M'×D' where D is the number of days

(6M + 6W )×24= (8M + 12W)×15

⇒( M + W) ×6×24 = (2M +3W) ×4×15

⇒( M+ W)12 = (2M +3W)5

⇒12M + 12W = 10M +15W

⇒2M = 3 W

hence, 2 men is equal to 3 women

2)now, 4M +6 W = ??

Applying M×D =M'×D'

(6M + 6W )×24 = (4M +6W ) ×D'

⇒(9W + 6W) ×24 = (6W +6W)×D'   ∵2M = 3 W

⇒15W ×24 = 12W ×D'

⇒D' = 30 days

It will takes 30 days to complete the same work by 4 men and 6 women