Formulate the following problems as a pair of equations, and hence find their solutions:
(ii) 2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone.
Let the number of days taken by a woman and a man be x and y respectively.
Therefore, work done by a woman in 1 day = 1/x
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) = 1/144-180
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
Hence, number of days taken by a woman = 18 and number of days taken by a man = 36
