Question

8 men and 12 women finish work in 10 day while 6 women and 8 men can finish it in 14 days. Find the time taken by the one women alone that by one men alone to finish the work.

Answer 1

$\huge\purple{Solution:}$

$\huge\bold{Let:}$

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

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

$\huge\bold{To Find}$

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

$\bold{\boxed{⇒X=1/140}}$

$\huge\bold{Hence}$

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

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

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Answer 2

✰Answer:-

• The time taken by 1 woman alone to finish the work = 140 days
• 1 man alone to finish the work = 280 days

step-by-step solution:-

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

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✪✪ Hence Answered ✪✪