# Ex.13.1 Q6 Direct and Inverse Proportions Solution - NCERT Maths Class 8

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## Question

In a model of a ship, the mast is $$9 \,\rm{cm}$$ high, while the mast of the actual ship is $$12\, \rm{cm}$$ high. If the length of the actual ship is $$28\;\rm{m}$$, how long is the model ship?

Video Solution
Direct And Inverse Proportions
Ex 13.1 | Question 6

## Text Solution

What is Known?

The mast is $$9 \,\rm{cm}$$ high while the mast of actual ships is $$12\, \rm{cm}$$ high.

What is Unknown?

If the length of the ship is $$28\;\rm{m}$$ How long is the model ship?

Reasoning:

Two numbers $$x$$ and $$y$$ are said in direct proportion if,

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

Where $$k$$ is a constant.

Steps:

 Actual ship Model ship $${y}_{1}=12\;\rm{m}$$ $${y}_{2}=9\;\rm{cm}$$ $${x}_{1}=28\rm{m}$$ $${x}_{2}=?$$

More the length of the ship more would be the length of its mast. Hence, this is a direct proportion.

\begin{align}\frac{{{x_1}}}{{{y_1}}} &= \frac{{{x_2}}}{{{y_2}}}\\\frac{{28}}{{12}} &= \frac{{{x_2}}}{9}\\12 \times {x_2} &= 28 \times 9\\{x_2} &= \frac{{28 \times 9}}{{12}}\\{x_2} &= 21\;{\rm{m}}\end{align}

Length of the model ship is $$21\;\rm{ m.}$$

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