Short Note

68 boxes of a certain commodity require a shelf-length of 13.6 m. How many boxes of the same commodity would occupy a shelf length of 20.4 m?

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#### Solution

Number of Boxes | 68 | x |

Shelf-length (in m) | 13.6 | 20.4 |

Let* x* be the number of boxes that occupy a shelf-length of 20.4 m.

\[\text{ If the length of the shelf increases, the number of boxes will also increase .} \]

\[\text{ Therefore, it is a case of direct variation } . \]

\[\frac{68}{x} = \frac{13 . 6}{20 . 4}\]

\[ \Rightarrow 68 \times 20 . 4 = x \times 13 . 6\]

\[ \Rightarrow x = \frac{68 \times 20 . 4}{13 . 6}\]

\[ = \frac{1387 . 2}{13 . 6}\]

\[ = 102\]

\[\text{ Thus, 102 boxes will occupy a shelf - length of } 20 . 4 m .\]

Concept: Concept of Direct Proportion

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