"Question 7 A batch of bottles was packed in 25 boxes with 12 bottles in each box. If the same batch is packed using 20 bottles in each box, how many boxes would be filled?
Class 8 Direct and Inverse Proportions Page 214"
Answers
Inverse variation:
Two quantities x and y are said to vary inversely or indirectly if an increase in x causes a decrease in y and a decrease in X causes an increase in y in such a way that xy remains constant.
In other words x and y are said to vary indirectly if x y = k, where K is a positive constant.
In inverse Proportion
xy= k
x=k/y
So we can find value of k from known values, and then use the formula to calculate the unknown values
When two quantities x and y are in direct proportion (or vary directly) they are also written as x∝y.
When two quantities x and y are in inverse proportion (or vary inversely) they are also written as x∝ 1/y
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Solution:
Table is in the attachment
Let the number of boxes filled, by using 20 bottles in each box, be x.
More the number of bottles, less will be the number of boxes.
Hence, the number of bottles and the number of boxes required to pack these are inversely proportional to each other.
Therefore,
12 × 25 = 20× x
x= (12 x 25)/20
x = (12 x 5)/4
x= 3 x 5 = 15 boxes
Hence, the number of boxes required to pack these bottles is 15.
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Hope this will help you....
