Question

two Men and five women can do a work in 12 days. 5 men and 2 women can do that
work in 9 days. Only 3 women can finish the same work in:
(a) 36 days (b) 21 days
(c) 42 days (d) 30 days​

Answer 1

$\huge \sf {\orange {\underline {\pink{\underline{Answer :-}}}}}$

Explanation:

$\Large{\underline{\sf{Given~that:}}}$

• 2 men and 5 women can do a work in 12 days
• 5 men and 2 women can do the work in 9 days

$\Large{\underline{\sf{To\:Find:}}}$

• Days taken by 3 women to complete the work

$\Large{\underline{\sf{Solution:}}}$

➝ Let the work done by one man in one day

= x

➝ Let the work done by one woman in one day

= y

★ By first case given,

    2 Men and 5 women can do a work in 12 days

    2x + 5y = 1/12 --------(1)

➝ By the second case,

    5 men and 2 women can finish the work in 9 days.

   5x + 2y = 1/9--------(2)

➝ Multiply first equation by 5 and second equation by 2

    10x + 25y = 5/12-------(3)

    10x + 4y = 2/9-------(4)

➝ Solving equation 3 and 4 by elimination method,

             21y = 5/12 - 2/9

             21y = (45 - 24)/108

             21 y = 21/108

              y = 1/108

             y = 1/108

➝ Hence one women can complete the work in 108 days.

➝ Work completed by 3 women is given by,

    Days taken by 3 women = ( 1/108 × 3)

    Days taken by 3 women = 36 days

    $\boxed{Days\:taken\:by\:3\:women=36\:days}$

➝ Hence option a is correct.

${\huge{\underline{\small{\mathbb{\pink{HOPE\:HELPS\:UH :)}}}}}}$

$\red{\tt{sωєєтcнαям♡~}}$

Answer 2

~Given that:

★ 2 men and 5 women can do a work in 12 days

★ 5 men and 2 women can do the work in 9 days

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~ToFind:

★ Days taken by 3 women to complete the work

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~Solution:

➝ Let the work done by one man in one day

= x

➝ Let the work done by one woman in one day

= y

★ By first case given,

2 Men and 5 women can do a work in 12 days

2x + 5y = 1/12 --------(1)

➝ By the second case,

5 men and 2 women can finish the work in 9 days.

5x + 2y = 1/9--------(2)

➝ Multiply first equation by 5 and second equation by 2

10x + 25y = 5/12-------(3)

10x + 4y = 2/9-------(4)

➝ Solving equation 3 and 4 by elimination method,

21y = 5/12 - 2/9

21y = (45 - 24)/108

21 y = 21/108

y = 1/108

y = 1/108

➝ Hence one women can complete the work in 108 days.

➝ Work completed by 3 women is given by,

Days taken by 3 women = ( 1/108 × 3)

Days taken by 3 women = 36 days

★Days taken by 3 women = 36days

➝ Hence option a is correct.

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