8 men and 12 women can do a piece of work in 9 days. 10 men and 20 women can do the same work in 6 days. How long will 5 men and 15 women take to do it?
Answers
8 men and 12 women can do a piece of work in 9 days
⇒ 8M + 12W = 9 days
10 men and 20 women can do the same work in 6 days
⇒ 10M + 20W = 6 days
Since both the work are the same:
(8 x 9)M + (12 x 9)W = (10 x 6)M + (20 x 6)W
72M + 108W = 60M + 120W
72M - 60M = 120W - 108W
12M = 12W
1 M = 1W
Find the amount of work 1 man can do:
10M + 20(1 M)= 6 days
10M + 20M = 6 days
30M = 6 days
1 M = 6 x 30
1M = 180 days
Find the amount of work 1 man can do in a day:
180 days = of the work
1 day = 1 ÷ 180 = 1/180 of the work
Find the amount of work 5 men and 15 women can do in a day:
5 + 15 = 20
1 man = 1/180 of the work
5 men and 15 women = 1/180 x 20 = 1/9 of the work
Find the number of days needed:
1/9 of the work = 1 day
9/9 of the work = 1 x 9 = 9 days
Answer: They need 9 days