Question

14 men can complete a piece of work in 3 days 21 women take 9 days to complete the same work .How many days will take for 1 man abd 6 women to complete

Answer 1

Answer:

18 days

Step-by-step explanation:

4M x 3 = 21W x 9

1M = 4.5W

To Find : 1M + 6W = __ days

1M + 6W = 4.5W + 6W = 10.5W

21 women takes 9 days to complete work

so, 10.5 women takes

= (21 x 9) / 10.5

= 18 days will take for 1 man and 6 women.

Answer 2

Given :

14 men can complete one work in 3 days.

21 women can complete one work in 9 days.

To find:

The number of days to complete one work by one man and six women.

Solution:

We know the formula for time and work,

(M₁ ×D₁ × H₁)/ W₁  = (M₂ × D₂ × H₂)/ W₂      ( formula 1 )

Using this formula,

14 Men × 3 days  = 21 women × 9 days        ( here, W₁= W₂ = 1)

1 women = (14 Men × 3 days) / (21 × 9)

6 women = ( 6 × 14 Men × 3 days) / (21 × 9)

6 women = (84÷63) men

Now,  1 man + 6 women = 1 man +  (84÷63) men = 1 + ( 4 ÷ 3)

= 7/3 men

Using formula 1,

14 Men × 3 days = 7/3 men ×  D days    ( Since W₁= W₂ = 1)

D days = 126 ÷ 7 = 18

Hence, the total number of days taken  by 1 man and 6 women = 18 days