Question

8 men take 10 days to pave a road. How long will 10 men take?

Answer 1

Answer:

10 men take=8*10/10days=8days

Answer 2

Given :-

• 8 men take 10 days to pave a road.

To Find :-

• How long will 10 men take?

Concept Used :-

Indirect Variation :-

• In inverse or indirect variation the variables change disproportionately or when one of the variables increases, the other one decreases. So behavior of the variables is just the opposite of direct variations. That is why it is called as Inverse or indirect variation. If x is in indirect variation with y, it can be symbolically written as x α 1/y.

• Two quantities x, and y, are said to be in inverse proportion if they fulfill the following criteria: If x increases, there is a decrease in y. If x decreases, there is an increase in y.

$\large\underline{\bold{Solution-}}$

Let number of days taken by 10 men be 'x' days.

As number of men increases, number of days decreases.

So, there is inverse variation between number of men and number of days.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf number \: of \: men & \bf number \: of \: days \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 8 & \sf 10 \\ \\ \sf 10 & \sf x \end{array}} \\ \end{gathered}$

So, using law of indirect variation, we have

8 × 10 = 10 × x

⇛ x = 8

Hence, 10 men take 8 days to pave the road.

Additional Information :-

Direct Variation :-

• If the values of two quantities depend on each other in such a way that a change in one quantity results in corresponding change in other, therefore if the ratio between the two variables remains constant, it is said to be in direct variation

Indirect or Inverse Variation :-

• Two quantities x, and y, are said to be in inverse proportion if they fulfill the following criteria: If x increases, there is a decrease in y. If x decreases, there is an increase in y.