Question

8 Women and 12 men can complete a work in 10 days while 6 women and 8 men can complete the same work in 14 days. Find the time taken by one woman alone and that one man alone to finish the work. What value is indicated from this action?

Answer 1

Let 1 woman finish the work in x days and 1 man finish the work in y days.
work done by 1 woman in 1 day = 1/x
work done by 1 man in 1 day = 1/y
ATQ

Case 1:
8 women and 12 men finish work in 10 days
1 day’s work of 8 women and 12 men= 1/10 part of  work.
8/x + 12/y = 1/10
4(2/x + 3/y) = 1/10
2/x + 3/y = 1/40……….(1)

Case 2.
6 women and 8 men finish work in 14 days
1 day’s work of 6 women and 8 men= 1/14 part of  work.
6/x + 8/y = 1/14
2(3/x + 4/y) = 1/14
3/x + 4/y = 1/28……….(2)

Putting 1/x = p and 1/y = q in equations,1 & 2 ,
2p + 3q = 1/40………….(3)
3p + 4q = 1/28………….(4)

Multiply equation 3 by 4 and equation 4 by 3,

8p + 12q = 4/40
8p +12q = 1/10…………..(5)
9p + 12q = 3/28………….(6)

On subtracting equation 5 and 6,
8p +12q = 1/10
9p + 12q = 3/28
(-)   (-)      (-)
-----------------
- p = 1/10-3/28
-p = (14 - 15)/140
-p = -1/140
p = 1/140

On substituting p= 1/140 in equation 5,
8p +12q = 1/10
8(1/140) +12q = 1/10
8/140 + 12q = 1/10
12q = 1/10 - 2/35
12q = (7 - 4)/70
12q = 3/70
q= 3/(70×12)
q= 1/(70×4)
q= 1/280

Now p= 1/140= 1/x
x = 140

q= 1/280= 1/y
y = 280

Hence, the  time  taken  by one  woman alone to finish the work = 140 days and  one man alone to finish the work = 280 days.

ii)Removal of gender discrimination &  woman Can work faster than man.

HOPE THIS WILL HELP YOU.

Answer 2

☆☆ranshsangwan☆☆

Here is the answer to your question.

Let 1 man alone can finish the work in x days and 1 woman can finish it in y days.

Then,

One man's one day's work =1/x
and one woman's one day's work =1/y

⇒ Eight man's one day's work =8/x
and 12 women' one day's work =12/y

8 men and 12 women can finish the work in 10 days.

∴ 8 men's and 12 women's one day work =1/10
thus
8/x+12/y= 1/10
= 80/x+120/y= 1 ..........e.q1

Again, 6 men and 8 women can finish the work in 14 days

6/x+8/y = 1/14

= 84/x+112/y = 1...........e.q(2)

On putting u= 1/x, v=1/y
in (1) and (2) we get

80u +120v = 1  ...(3)

84u + 112v = 1  ...(4)

On solving (3) and (4), we get

u = 1/140 = 1/x= x= 140

v= 1/280= 1/y = y= 280


Thus, 1 man alone can finish the work in 140 days and 1 woman alone can finish the same work in 280 days.

Cheers..!!