Question

if 12 workers take 70 day to complete one work how many days will 21 workers take to complete the same work ​

Answer 1

Given:-

• 12 workers take 70 days to complete one work.

To Find:-

• In how many days will 21 workers complete the same work =?

Solution:-

$\sf \therefore \: 12 \: workers \: take \: days \: to \: complete \: a \: work \: in = 70 \: days \\ \\ \sf 1 \: worker \: take \: days \: to \: complete \: a \: work \: in \: = \frac{70}{12} \\ \\ \sf \because \: 21 \: workers \: take \: days \: to \: complete \: a \: work \: in \: = \frac{70}{12} \times 21 \\ \\ \sf \implies \: 122 \frac{1}{2} days$

Hence, 21 workers complete a work in $\sf122\frac{1}{2}$days.

Answer 2

Solution :-

Let the Required Number of Days be x.

Then, we have the Following Table :

$\begin {tabular}{| l |c|c|} \cline {1 - 3} Number of Workers & 12 & 21\\\cline {1 -3} Number of Days & 70 & \textbf {x}\\\cline {1- 3} \end {tabular}$

Clearly, More Men will take Less Days to Finish the Work.

So, it is a Case of Inverse Proportion.

$\begin {gathered} \end {gathered}$$\begin {gathered} \end {gathered}$

$\begin {aligned} \therefore 12 \times 70 = 21 \times x & \Longrightarrow 12 \times 70 = 21x\\\\& \Longrightarrow \bold x = \dfrac{12 \times 70}{21} = \bold {40} \end {aligned}$

∴ The 21 Workers would take 40 Days to Complete the Work . . .

$\begin {gathered} \end {gathered}$

Additional Information :-

Inverse Proportion :- Two Quantities x and y are said to be in Inverse Proportion if xy = k, where k is a Constant.

Thus, $\mathtt {x_1 y_1 = x_2y_2 = x_3y_3 = . . . . . = k}$