We will learn ‘what inverse variation is’ and how to solve different types of problems on some situations of inverse variation.
If two quantities are related in such a way that increase in one quantity causes corresponding decrease in the other quantity and vice versa, then such a variation is called an inverse variation or indirect variation.
If the two quantities are in inverse variation then we say that they are inversely proportional.
Suppose, if two quantities x and y vary inversely with each other, then the values of x is equal to the inverse ratio of the corresponding values of y.
i.e., \(\frac{x_{1}}{x_{2}} = \frac{y_{2}}{y_{1}}\)
or, \(x_{1} \times y_{1} = x_{2} \times y_{2}\)
Some situations of inverse variation:
● More men at work, less time taken to finish the work.
Less men at work, more time is taken to finish the work.
● More speed, less time is taken to cover the same distance.
Less speed, more time is taken to cover the same distance.
Problems on different situations of inverse variation:
1. If 48 men can do a piece of work in 24 days, in how many days will 36 men complete the same work?
Solution:
This is a situation of indirect variation.
Less men will require more days to complete the work.
48 men can do the work in 24 days
1 man can do the same work in 48 × 24 days
36 men can do the same work in (48 × 24)/36 = 32 days
Therefore, 36 men can do the same work in 32 days.
2. 100 soldiers in a fort had enough food for 20 days. After 2 days, 20 more soldiers join the fort. How long will the remaining food last?
Solution:
More soldiers, therefore, food lasts for less days.
This is a situation of indirect variation.
Since 20 soldiers join the fort after 2 days, therefore, the remaining food is sufficient for 100 soldiers and 18 days.
`Situations of Direct Variation
Situations of Inverse Variation
Direct Variations Using Unitary Method
Direct Variations Using Method of Proportion
Inverse Variation Using Unitary Method
Inverse Variation Using Method of Proportion
Problems on Unitary Method using Direct Variation
Problems on Unitary Method Using Inverse Variation
Mixed Problems Using Unitary Method7th Grade Math Problems
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