Question

4 men and 6 women complete a work in 8 days, 2 men and 9 women also complete in 8 days. The number of days in which 18 women complete the work is : 

(a) 16/3 days 

(b) 17/3 days 

(c) 13/3 days 

(d) 14/3 days

Answer 1

Correct option (a) 16/3 days

Explanation:

Given

⇒ 4m +6w → 8 days 

⇒ 32m + 48w → 1 day……(i) 

⇒ 2m + 9w → 8 days 

⇒16m + 72w → 1 day3………….(ii) 

⇒ From equation (i) = (ii) 

⇒ 32m + 48w = 16m +72w 

⇒ 32m – 16m = 72w – 48w 

⇒ 2m = 3w 

⇒Here, it is given that a group of 4 m +6 women can do the work in 8 days, converting the whole equation into women. 

⇒ 4m + 6w → 8 days 

⇒ (2 ×2m)+6w → 8 days 

⇒ (2×3w)+6w → 8 days 

⇒ 6w + 6w → 8days 

⇒ 12w → 8 days 

i.e. 12 women can do the work in 8 days 

⇒ Then a group of 18 women can do the work