The work done by a woman in 8, text{hours} is | vedclass

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(B) Given that the work done by $1$ woman in $8\, 	ext{hours} = 1$ man in $6\, 	ext{hours} = 1$ boy in $12\, 	ext{hours}$.Let the work rate of a ma

Vedclass · Accepted Answer

$1 \frac{1}{2}$

Vedclass · Answer

(B) Given that the work done by $1$ woman in $8\, 	ext{hours} = 1$ man in $6\, 	ext{hours} = 1$ boy in $12\, 	ext{hours}$.Let the work rate of a man be $M$,a woman be $W$,and a boy be $B$.$8W = 6M = 12B$.From $6M = 12B$,we get $M = 2B$.From $8W = 6M$,we get $8W = 6(2B) = 12B$,so $W = 1.5B$.We need to find the work done by $12$ men,$12$ women,and $12$ boys in terms of men:$12$ men $+ 12$ women $+ 12$ boys $= 12$ men $+ (12 	imes \frac{6}{8})$ men $+ (12 	imes \frac{6}{12})$ men.$= 12 + 9 + 6 = 27$ men.Using the formula $M_1 D_1 t_1 = M_2 D_2 t_2$:$9 	imes 6 	imes 6 = 27 	imes D_2 	imes 8$.$324 = 216 	imes D_2$.$D_2 = \frac{324}{216} = \frac{3}{2} = 1 \frac{1}{2}$ days.

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