Question

2 women and 5 men can together finish a piece of embroidery in 4 days, while 6 men and 3 women can finish it in 3 days. Find the time taken by 1 woman alone to finish the embroidery and that taken by a man alone.

Answer 1

Taking 1 day work in both the cases,

(2W + 5M = 1/4)*6
(3W + 6M = 1/3)*5

12W + 30M = 3/2
15W + 30M = 5/3
(-)    (-)          (-)

-3W = -1/6
1W = 1/18

1 day work of 1 woman =1/18

Therefore, 1 woman can the finish embroidery in 18 days.

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Answer 2

Answer:

Step-by-step explanation:

Solution:-

Let the number of days taken by a woman and a man be x and y.          According to the question,                  

⇒ 4(2/x + 5/y) = 1                  

⇒ 2/x + 5/y = 1/4                  

⇒ 3(3/x + 6/y) = 1                  

⇒ 3/x + 6/y = 1/3                  

Putting 1/x = p and 1/y = q in these equations, we get                  

⇒ 2p + 5q = 1/4                 

By cross multiplication, we get                  

⇒ p/-20 - (-18) = q/-9 - (-18) = 1/144b- 180                  

⇒ p/-2 = q/-1 = 1/-36                  

⇒ p/-2 = - 1/36 and q/-1 = 1/-36                  

⇒ p = 1/18 and q = 1/36                  

⇒ p = 1/x = 1/18 and q = 1/y = 1/36                  

⇒ x = 18 and y = 36

Number of days taken by a woman = 18

Number of days taken by a man = 36