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

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## 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.

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