# Ex.13.2 Q5 Direct and Inverse Proportions Solution - NCERT Maths Class 8

## Question

A farmer has enough food to feed \(20\) animals in his cattle for \(6\) days. How long would the food last if there were \(10\) more animals in his cattle?

## Text Solution

**Reasoning:**

Two numbers \(x\) and \(y\) are said to vary in inverse proportion if

\[\begin{align}xy = {\rm{ }}k,{\rm{ }}x{\rm{ }} = {\rm{ }}\frac{1}{y}k\end{align}\]

Where \(k\) is a constant.

\[\begin{align}{x_1}{y_1} = {x_2}{y_2}\end{align}\]

**What is Known:**

In a cattle, food is for \(20\) animals for \(6\) days.

**What is Unknown:**

The number of days for \(30\) animals \((20 + 10 = 30)\)

**Steps:**

If the number of animals increases the number of days they can be fed will decrease, so it is in the inverse proportion.

\[\begin{align}{x_1}{y_1}& = {x_2}{y_2}\\20 \times 6 &= 30 \times {y_2}\\{y_2} &= \frac{{20 \times 6}}{{30}}\\{y_2} &= 4\end{align}\]

The food would last for \(4\) days for \(30\) animals.