Question

2 ladies and 5 gents complete an embroidery work in 4 days, while 3 ladies and 6 gents can complete it in 3 days. Find out how many days a single lady can take to complete it. again how much time a single man will take to complete it?

Answer 1

Let the time taken by single men be x and time taken by single lady be y

Then,

2/y+5/x=1/4

3/y+6/x=1/3

Let 1/y=u and 1/x=v

Then,

2u+5v=1/4.........>8u+20v=1........(1)

3u+6v=1/3........>9u+18v=1

9u=1-18v

u=(1-18v)/9.......(2)

(2)in(1)

8(1-18v)/9+20v=1

8-144v+180v=9

36v=1

V=1/36=1/x......(3)

X=36

(3)in(1)

8u+20/36=1

8u=4/9

U=4/9*8=1/18=1/y

Y=18

Hope it helps....