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.