"Question 5 A farmer has enough food to feed 20 animals in his cattle for 6 days. How long would the food last if there were 10 more animals in his cattle?
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 days that the food will last if (20+10)= 30 animals in the cattle be x
More the number of animals, less will be the number of days for which the food will last.
Hence, the number of days the food will last & the number of animals are inversely proportional to each other.
Therefore,
20 × 6 = 30 × x
X=( 20×6)/30
X= 2× 2= 4
X= 4 days
Hence, the food will last for 4 days.
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