2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish in 3 days.find the time taken by 1 women alone to finish the workand also that by 1 man alone.
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let the days needed to complete by women be x and men be y
then work done in i day=1/x and 1/y respectively
from equation 1, 2/x+5/y=1/4
from equation 2, 3/x+6/y=1/3
let 1/x=a and 1/y=b
eq.1 2a+5b=1/4 => multiplying with 4, 8a+20b=1 (eq 4)
eq.2 3a+6b=1/3 => multiplying with 3, 9a+18b=1 (eq 5)
eq4*9=72a+180b=9
eq5*8=72a+144b=8
eq4-eq5=36b=1
b=1/36
sub. b=1/36 in eq4
72a +180*1/36=9
72a +5=9
72a=4
a=1/18
women=>1/x=a=>1/x=1/18=>x=18
men=>1/y=b=>1/y=1/36=>y=36
then work done in i day=1/x and 1/y respectively
from equation 1, 2/x+5/y=1/4
from equation 2, 3/x+6/y=1/3
let 1/x=a and 1/y=b
eq.1 2a+5b=1/4 => multiplying with 4, 8a+20b=1 (eq 4)
eq.2 3a+6b=1/3 => multiplying with 3, 9a+18b=1 (eq 5)
eq4*9=72a+180b=9
eq5*8=72a+144b=8
eq4-eq5=36b=1
b=1/36
sub. b=1/36 in eq4
72a +180*1/36=9
72a +5=9
72a=4
a=1/18
women=>1/x=a=>1/x=1/18=>x=18
men=>1/y=b=>1/y=1/36=>y=36
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