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 Method**7th Grade Math Problems**

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