4 male and 6 female do a piece of work in 20 days while 6 male and 4 female can do the same work in16 days. In how many days can 4 male and 2 female do the work? a) 3 62/142 b) 2 18/124 c) 4 81/165 d) 1 67/133
D
Let 1 male’s 1 day’s work = x
1 female’s 1 day’s work = y
Then 4x + 6y = 1/20 ---------->A
80x + 120y = 1 -----------1
6x + 4y = 1/16 ----------B
96x + 64y = 1 --------2
Multiply 1 by 96 7680x + 11520y = 96 ----3
Multiply 2 by 80 => 7680x + 5120 y = 80 -----4
Subtracting above equation
6400y = 16
Y= 16/6400 = 1/400
Substitute y value in B
6x +4 (1/400) = 1
6x+1/100 = 1
6x = 1 – 1/100 = 99/100
X=99/(100*6) = 33/200
(4 male + 2 female)’s 1 day work = 4x+ 2y
=4(33/200)+2(1/400)
=132/200+1/200 = 133/200
So 4 male and 2 female together can finish the work in 200/133 = 1 67 /133 days