Formulate the following problems as a pair of equations, and hence find their solutions:
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.
Solution
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 ` 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 `
`p = 1/18 `
`p = 1/x = 1/18 `
x = 18 and y = 36
Hence, number of days taken by a woman = 18 and number of days taken by a man = 36
