Question

8 women and 12 men can together finish an embroidery work in 10 days, while 6 women and 8 men can finish it in 14 days. Find the time taken by 1 woman alone to finish the work, and also that taken by 1
man alone.​

Answer 1

Given:

• 8 women and 12 men can together finish an embroidery work in 10 days
• 6 women and 8 men can finish it in 14 days

To find:

Time taken by 1 woman alone and 1 man alone to complete the task

Solution:

As per the data given in the question:

• (8W+12M)10 = (6W+8M)14
• 40W+60M = 42W+56M
• 4M =  2W
• 2M = W -----------(I)

Time taken by 1 woman

Let work will be finished in D days.

• (8W+12M)10 = (W)D

from equation (I)

• (8W + 6W)10 = WD
• (14W)10 = WD
• 140W = WD
• D = 140

Time taken by 1 man:

Let work will be finished in D' days.

• (8W+12M)10 = (M)D'

from equation (I)

• (16M + 12M)10 = MD'
• (28M)10 = MD'
• 280M= MD'
• D' = 280

Time taken by 1 woman alone and 1 man alone to complete the task is 140 days and 280 days respectively.