Question

2 Men and 5 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

Answer:

$\bigstar{\bold{Option\:a:\:36\:days}}$

Step-by-step explanation:

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

• 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 work done by one man in one day = x

➝ Let 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

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

➝ Hence option a is correct.