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?

 

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.