# Ex.13.2 Q4 Direct and Inverse Proportions Solution - NCERT Maths Class 8

## Question

If a box of sweets is divided into \(24\) children, they will get \(5\) sweets each. How many would each get, if the number of children is reduced to \(4\)?

## Text Solution

**What is Known?**

\(24\) children get \(5\) sweets each.

**What is Unknown?**

No. of sweets getting by \(20\) children. \([24 – 4 = 20]\)

**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.

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

**Steps:**

If the number of children will decrease, the number of sweets they get will increase. Hence it is the inverse proportion.

\[\begin{align}{x_1}{y_1} &= {x_2}{y_2}\\24 \times 5 &= 20 \times {y_2}\\{y_2} &= \frac{{24 \times 5}}{{20}}\\{y_2}& = 6\end{align}\]

Hence \(20\) children will get \(6\) sweets each.