Question

Six cows can graze a field in 28 days. How long would 14 cows take to
graze the same field?

Answer 1

Given :-

• Six cows can graze a field in 28 days.

To Find :-

• How long would 14 cows take to graze the same field?

Concept Used :-

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.

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

Let 14 cows take 'x' days to graze the same field.

Since,

as number of cows increases, there is decrease in number of days.

⇛ There is inverse variation between number of cows and number of days.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf number \: of \: cows & \bf number \: of \: days \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 6 & \sf 28 \\ \\ \sf 14 & \sf x \end{array}} \\ \end{gathered}$

So,

By using the law of inverse variation,

we have

6 × 28 = 14 × x

⇛ x = 12 days

Hence, 14 cows can graze the same field in 12 days.

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