Question

8 women and 12 men can together finish an embroiderywork in 10 days while 6 women and 8 men can finish it in 14 days. find the time taken by one women alone to finish the workand also that taken by 1man alone

Answer 1

|| ✰✰ ANSWER ✰✰ ||

Let

1 woman finish the work in X days

1 man finish the work in Y days

Now,

Work done by 1 woman in 1 day = 1 / X

Work done by 1 man in 1 day = 1 / Y

1st Part :-

8 women and 12 men finish work in 10 days ( Given )

1 day work of 8 women and 12 men = 1 / 10 of total work

Now,

8 / X + 12 / Y = 1 / 10

4 ( 2 / X + 3 / Y ) = 1 / 10

2 / X + 3 / Y = 1 / 40

2nd Part :-

6 women and 8 men finish work in 14 days ( Given )

1 day work of 6 women and 8 men = 1 / 14 of total work

Now,

6 / X + 8 / Y = 1 / 14

2 (3 / X + 4 / Y ) = 1 / 14

3 / X + 4 / Y = 1 / 28

Now,

Putting 1 / X = p and 1 / Y = q in Part 1st & 2nd

2p + 3q = 1 / 40 ( 1 )

3p + 4q = 1 / 28 ( 2 )

Multiply equation 1 by 2 and equation 2 by 1

8p + 12q = 4 / 40

8p +12q = 1 / 10 ( 3 )

9p + 12q = 3 / 28 ( 4 )

On subtracting equation 3 and 4

8p +12q = 1/10

9p + 12q = 3/28

Calculation :-

- p = 1 / 10 - 3 / 28

-p = ( 14 - 15 ) / 140

-p = -1 / 140

p = 1 / 140

Now,

Substituting p= 1 / 140 in equation 3

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

So, Y = 140

q = 1 / 280 = 1 / Y

Y = 280

Therefore, The time taken by

1 woman alone to finish the work = 140 days

1 man alone to finish the work = 280 days

✪✪ Hence Answered ✪✪

Answer 2

$\huge\purple{Solution:}$

Let:

The time taken by 1 women be 1/X in 1day

The time taken by 1 man be 1/Y in day

To Find

Time taken by 1 women and man alone.

Given, 8 women and 12 men can together finish an embroiderywork in 10 days.

⇒8X+12Y=1/10-------(1)

Given,6 women and 8 men can finish it in 14 days.

⇒6X+8Y=1/14---------(2)

Now , solving equation 1 and 2 by multiplying than subtracting eachother.

in equation 1 multiplying by 1/6 and equation 2 multiplying by 1/8

⇒48X+72Y=1/10

⇒1/48X+1/64Y=1/14

• BY solving we get,

⇒72Y-64Y=1/10-1/14

⇒8Y=7-5/70

⇒8Y=2/70

⇒4Y=1/70

⇒Y=1/280

• Putting the value of Y=1/280 in EQ 1

⇒8X+12×1/280=1/10

⇒8X+3/70=1/10

⇒8X=1/10-3/70

⇒8X=7-3/70

⇒8X=4/70

⇒X=1/140

Hence,

The time taken by one woman to finish the work=280days

The time taken by one man to finish the work=140days