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?

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:

\[{{\bf{Actual\; ship}}}\] \[{{\bf{Model\; ship}}}\]
\({y}_{1}=12\;\rm{m}\) \({y}_{2}=9\;\rm{cm}\)
\({x}_{1}=28\rm{m}\) \({x}_{2}=? \)

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 \(21\;\rm{ m.}\)