Question

8 women and 12 men can together
finish a work in 10 days, while 6
women and 8 men can finish it in 14
days. Find the time takenby 1
woman alone to finish the work, and

also that taken by 1 man alone.​

Answer 1

Step-by-step explanation:

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.

HOPE THIS WILL HELP YOU.

PLEASE mark as brainliest!!