Question

3 men and 6 women finish a job in 9 days, while 2 men and 8 women finish it in 12 days. in how many days will 12 women working alone finish the same job?

Answer 1

3M+6W=== 9 days== 1 work
2M+8W====12 days== same work
Total Work = People*Efficiency * Days
(3M+6W)*9 = (2M+8W)*12
(3M+6W)*3 = (2M+8W)*4
9M + 18W = 8M + 32W
M = 14 W
M:W = 14:1

Now, find total work:
(3M+6W)*9 = Total Work [The other one can also be used, that is: (2M+8W)*12]
(3*14 + 6*1)* 9 = 48*9 = 432
Total work = 432
No: of women = 12
Efficiency per women = 1
No:*Efficiency*Days = Work
12*1*Days = 432
Days = 36
Hence 12 women take 36 days to complete the work.
Hope it helps.

Answer 2

Concept:

Linear equations are first-order equations. In the coordinate system, linear equations are defined for lines. A linear equation in one variable is defined as an equation with a homogeneous variable of degree 1 (i.e. only one variable). There might be more than one variable in a linear equation. If there are two variables in a linear equation, it is referred to as linear equations in two variables, and so on.

Find:

The days it takes for women to finish the work.

Solution:

$3M+6W=9 days\\2M+8W=12 days$

Total Work = People*Efficiency * Days

$(3M+6W)*9 = (2M+8W)*12\\M = 14 W\\M:W = 14:1$

$Total Work= (3M+6W)*9 \\Total Work= (3*14 + 6*1)* 9 \\ Total Work=48*9 \\Total Work=432$

$No.of dats*Efficiency*Days = Work\\12*1*Days = 432\\Days = 36$

Hence, it takes $36$ days to complete the work.

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