sixteen men can finish a work in 8 days. Eight men and nine women working together can finish the same work 10 days. In how many days will Twenty women finish same work ?
Answers
Answer:
12 days
Step-by-step explanation:
Men working alone
Fraction 16 men complete in a day = 1/8
Fraction each man completes in a day = 1/8÷16 = 1/128
Men and women working together
Fraction done by 8 men / day = 1/128x 8 = 1/16
Fraction done by the men in 10 days = 1/16 x 10 = 5/8
Remaining fraction done by women = 1 - 5/8 = 3/8
Fraction done by the women in 1 day = 3/8 ÷ 10 = 3/80
Fraction done by one woman per day = 3/80 ÷ 9 = 1/240
Women working alone
Fraction done by 20 women in one day = 1/240 x 20 = 1/12
Number of days taken by the 20 women to do the work
= 1 ÷ 1/12
= 12 days
Twenty women can complete the work in 10 days.
Sixteen men can finish work in = 8 days
Eight men and nine women can do in = 10 days
Hence,
16 men + 12 women complete the work in 8 days and
20 men complete the work in 16 days.
Therefore,
= 16 × 8 men + 12 × 8 women
= 20 × 16 men
= 128 men + 96 women ≡ 320 men
Thus, 96 women = 192 men
Now,
= 1 woman = 2 men
Therefore, 16 women = 32 men
= M1D1 = M2D2
= 20×16 = 32×D2
= D2 = 20 × 16 / 32
= 320/32
= 10
thus, work can be completed in 10 days.