18 men and 36 women can level an area of 810 sq. in 6 days. The ratio of the areas that each man and each woman can level in the same amount of time is `3:1`. Find the number of dayss is which 22 men adn 14 women can level an area of 120 sq. m.

Options

A. 8
B. 12
C. 9
D. 10

Answer

D

Explanation

Let the areas that each man and each woman can level (in sq. m.) b m/day and q/day respectively.
Area that 18 men and 36 women can level each day `=(18m+36w)` sq.m.
`:. 6(18m+36w)=810`
`18m+36w=135`
Given : `(m)/(w)=(3)/(1), i.e.,m=3w`
`:. 18(3w)+36w=135`
`90w-135`
`w=(3)/(2)`
`:. m=(9)/(2)`
Let the required number of days be d
`d(22m+14w)=1200`
`d(22((9)/(2))+14((3)/(2)))=1200`
`rArr120 d=122 rArrd=10`