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What number must be added to each of the numbers \[\mathbf{15},\text{ }\mathbf{17},\text{ }\mathbf{34}\text{ }\mathbf{and}\text{ }\mathbf{38}\] to make them proportional?
What number must be added to each of the numbers \[\mathbf{15},\text{ }\mathbf{17},\text{ }\mathbf{34}\text{ }\mathbf{and}\text{ }\mathbf{38}\] to make them proportional?
Class 10 | Exercise 1 | ICSE | Maths | ML Aggarwal | Ratio and Proportion
What number must be added to each of the numbers \[\mathbf{15},\text{ }\mathbf{17},\text{ }\mathbf{34}\text{ }\mathbf{and}\text{ }\mathbf{38}\] to make them proportional?

Consider x be added to each number

So the numbers will be

\[15\text{ }+\text{ }x,\text{ }17\text{ }+\text{ }x,\text{ }34\text{ }+\text{ }x\text{ }and\text{ }38\text{ }+\text{ }x\]

Based on the condition

\[\left( 15\text{ }+\text{ }x \right)/\text{ }\left( 17\text{ }+\text{ }x \right)\text{ }=\text{ }\left( 34\text{ }+\text{ }x \right)/\text{ }\left( 38\text{ }+\text{ }x \right)\]

By cross multiplication

\[\left( 15\text{ }+\text{ }x \right)\text{ }\left( 38\text{ }+\text{ }x \right)\text{ }=\text{ }\left( 34\text{ }+\text{ }x \right)\text{ }\left( 17\text{ }+\text{ }x \right)\]

By further calculation

\[570\text{ }+\text{ }53x\text{ }+\text{ }{{x}^{2}}~=\text{ }578\text{ }+\text{ }51x\text{ }+\text{ }{{x}^{2}}\]

So we get

\[\begin{array}{*{35}{l}}

{{x}^{2}}~+\text{ }53x\text{ }\text{ }{{x}^{2}}~\text{ }51x\text{ }=\text{ }578\text{ }\text{ }570  \\

2x\text{ }=\text{ }8  \\

x\text{ }=\text{ }4  \\

\end{array}\]

Hence, \[4\] must be added to each of the numbers.

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