Ex.13.1 Q4 Direct and Inverse Proportions Solution - NCERT Maths Class 8

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Question

A machine in a soft drink factory fills \(840\) bottles in \(6\) hours. How many bottles it will fill in five hours?

 Video Solution
Direct And Inverse Proportions
Ex 13.1 | Question 4

Text Solution

What is Known?

\(840\) bottles can be filled in \(6\) hours.

What is Unknown?

Bottles filled in \(5 \) hours.

Reasoning:

Two numbers \(x\) and \(y\) are said to be in direct proportion, if

\[\begin{align}\frac{x}{y}=k,\quad x=y\,k\end{align}\]

Where \(k\) is a constant.

Steps:

No of bottles Time in hours
\({x}_{1}=840\) \({y}_{1}=6\)
\({x}_{2}=?\) \({y}_{2}=5\)

 

So, the number of bottles filled, and numbers of hours are directly proportional to each other.

\[\begin{align}  \frac{{{x}_{1}}}{{{y}_{1}}}&=\frac{{{x}_{2}}}{{{y}_{2}}} \\  \frac{840}{6}&=\frac{{{x}_{2}}}{5} \\  6{{x}_{2}}&=840\,\times \,5 \\  {{x}_{2}}&=\frac{840\times 5}{6} \\  {{x}_{2}}&=700 \end{align}\]

\(700 \) bottles will be filled in \(5 \) hours.