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 us consider,
Number of days taken by women to finish the work = x
Number of days taken by men to finish the work = y
Work done by women in one day = 1/x
Work done by women in one day = 1/y
As per the question given,
4(2/x + 5/y) = 1
(2/x + 5/y) = 1/4
And, 3(3/x + 6/y) = 1
(3/x + 6/y) = 1/3
Now, put 1/x=m and 1/y=n, we get,
2m + 5n = 1/4 => 8m + 20n = 1 …………………(1)
3m + 6n =1/3 => 9m + 18n = 1 ………………….(2)
Now, by cross multiplication method, we get here,
m/(20-18) = n/(9-8) = 1/ (180-144)
m/2 = n/1 = 1/36
m/2 = 1/36
m = 1/18
m = 1/x = 1/18
or x = 18
n = 1/y = 1/36
y = 36
Therefore,
Number of days taken by women to finish the work = 18
Number of days taken by men to finish the work = 36