The portion of work done by one man in one day = 1x
Let the time taken by one woman to finish the work = y days .The portion of work done by one woman in one day = 1y Now, 8 men and 12 women can finish the work in 10 days. So the portion of work done by 8 men and 12 women in one day = 110 (1) Also, the portion of work done by 8 men in one day is 8 × 1x. = 8x Similarly, the portion of work done by 12 women in one day is 12 × 1y= 12y Total portion of work done by 8 men and 12 women in one day = 8 12+ (2)x yæ ö Equating equations (1) and (2) 8 12 1ç ÷ + =è ø10x y æ ö 10 8 12ç ÷ +è ø = 1x y80 120+ = 1 (3)x yAlso, 6 men and 8 women can finish the work in 14 days .The portion of work done by 6 men and 8 women in one day = 68 1+ =14x y æ ö Þ 146 8ç ÷ +è ø = 1x yæ ö 84 112ç ÷ +è ø = 1 (4)x y