Question

2 women and 5 men can together finish an embroidery work in 4 days while 3 womens abd 6 nens can finish in 3 days find the te talen by 1 women alone and by 1 men alone

Answer 1

let the work of women be x.
let the work of manln be y.

Therefore,
let both in one day be,
2/x + 5/y = 1/4............... (i)
condition 2:
3/x + 6/y = 1/3......... (ii)

let 1/x be a and 1/y be y.

from (I) and (ii),
(2a +5b =1/4) * 3
(3a + 6b = 1/3) * 2

6a +15b = 3/4. ( subtract (ii) from (i) )
6a +12b = 2/3

3b= 3/4 - 2/3
3b= 9-8/12
b= 1/12*3
b = 1/ 36
therefore,
1/y = b
y = 1/b
y = 36 days

2a + 5b = 1/4
2a + 5 / 1/36 = 1 /4
(72a + 5)/36=1/4
72a + 5 =9
72a = 4
a = 4/72
a = 1/18

1/x = a
x= 18


therefore work of one man is 36 days and work of one woman is 18 days.

Answer 2

because. in 4days work done by 2women+5men
so., in 1day work done by =4(2women+5men)
=8women +20men
NOW,
because. in3days work done by 3women +6men
so. in1day work done by 3(3women +men)
=9women +18men

so
=>8women +20men=9women +18men
=>(20-18)men=(9-8)women
=>1women =2men

so
2women +5men =2x2men +5men=9men
so. 1women +1men =3men

because
9men do work in 4days
so. 1men do that works in9 x 4days
so. 1man alone do that in 36 days
so. 1women (2men) that work in 36/2=18days
ANSWER