Question

2 men and 7 women can do a piece of work in 4 days, while 4 men and 4 women can do the same work in 3 days . How many would it take one men and one women to do it ?

Answer 1

Step 1 :Assigning the variables

To represent the unknown quantities by two variables.

let 1st man finish the work in x days and 1 woman in y days

Therefore , 1 man's 1 days work = 1/x

and 1 woman one days work = 1/y

Step 2: Framing Equation

According to the question

$$\begin{gathered} \frac{2}{x}+\frac{7}{y}=\frac{1}{4}........\left(1\right) \\ \frac{4}{x}+\frac{4}{y}=\frac{1}{3}........\left(2\right) \end{gathered}$$

Step 3 : Elimination method

Solving with suitable method (elimination)

Multiplying equation (1) by (2) ,

It becomes

$$\begin{gathered} 1x2\Rightarrow \frac{4}{x}+\frac{14}{y}=\frac{2}{4}\to 3 \\ \frac{4}{x}+\frac{4}{y}=\frac{1}{3}\to 2 \end{gathered}$$

Subtracting equation 2 from equation 3 we get

$$\begin{gathered} 3-2\Rightarrow 0+\frac{14}{y}-\frac{4}{y}=\frac{2}{4}-\frac{1}{3} \\ \frac{10}{y}=\frac{6-4}{12}=\frac{2}{12}=\frac{1}{6} \\ \frac{10}{y}=\frac{1}{6}\Rightarrow \\ y=60days \end{gathered}$$

Step 4 : Substituting values

substitute the value of y = 60 in equation 1

we get ,

$$\begin{gathered} \frac{2}{x}+\frac{7}{60}=\frac{1}{4} \\ \frac{2}{x}-\frac{1}{4}-\frac{7}{60}\Rightarrow \frac{8}{60} \\ \frac{2}{x}=\frac{8}{60} \\ x=\frac{2x60}{8} \\ x=15days \end{gathered}$$

Hence ,1st man can finish the work in 15 days and 1st woman can finish the work in 60 days .