Question

If 12 men or 18 women harvest a field in 14 days, then in how many days
will 8 men and 16 women harvest the field together?

Answer 1

12 men can reap the field in 14 day

⇒ 1 man can reap the field in 12 x 14 = 168 days

⇒ 8 men can reap the field in 168 ÷ 8 = 21 days

⇒ 1 day =1 ÷ 21 =  1/21 of the field

18 women can reap the field in 14 day

⇒ 1 woman can reap the field in 18 x 14 = 252 days

⇒  16 women can reap the field in 252 ÷ 16 = 15.75 of the field

⇒  1 day = 1 ÷ 15.75 = 4/63 of the field

 

So in one day, 12 men and 18 women can reap:

1/21 + 4/63 = 1/9 of the field

Find the number of days needed:

1/9 fo the field = 1 day

9/9 of the field = 1 x 9 = 9 days

Answer: They will take 9 days to reap the field.