Question

8 women and 5 men can together finish a work in 10 days, while 6 women and 8 men finish in 14 days. Find the time taken by 1 women alone to finish the work, and also that taken by 1 man alone​

Answer 1

Step-by-step explanation: 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