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Question
The boxes are to be filled with apples in a heap. If 24 apples are put in a box then 27 boxes are needed. If 36 apples are filled in a box how many boxes will be needed?
Solution
If the number of apples in a box is increased, then the number of boxes decreases. So, the number of apples filled in the box and the number of boxes are in inverse proportion.
Let the number of apples filled in a box be x and the number of boxes be y.
Here, x varies inversely as y, i.e., `x α 1/y`.
∴ \[x = \frac{k}{y}\] , where k is constant of variation
⇒ x × y = k
When x = 24, y = 27.
∴ k = 24 × 27 = 648
So, the equation of variation is xy = 648.
When x = 36,
36y = 648
⇒ y = \[\frac{648}{36}\] = 18
Thus, the number of boxes needed is 18.
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