# 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.

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