Direct variation is the relationship of two variables such that a variable increases/decreases in its value as the other variable increases/decreases i.e the two variables are proportional to each other. In other words, it is defined as the mathematical expression that shows the relationship between two variables whose ratio is constant.

The**Direct Variation Formula** is,

The

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Some solved problems on direct variation are given below:

### Solved Examples

**Question 1: **The amount of wooden box made is directly proportional to the number of wooden block. The number of wooden block needed for 20 box is 100. How much wooden blocks are needed for a box ?

** Solution: **

In the given problem,

Number of wooden blocks needed for 20 boxes = y = 100

Number of boxes = x = 20

Number of wooden blocks needed for a box = k

The direct variation formula is,

y = k * x

100 = k * 20

k = $\frac{100}{20}$

k = 5

Number of wooden blocks needed for a box = 5

**Question 2: **The amount of sweets sold is directly proportional to the number of customers. The amount of sweet sold for 5 customers was for $\$$20. How much money is earned from each customer ?

** Solution: **

In the given problem,

Amount of sweet sold to 5 customers = y = $\$$20

Number of Customers = x = 5

Amount of sweet sold to a customer = k

The direct variation formula is,

y = k * x

20 = k * 5

k = $\frac{20}{5}$

k = 4

Amount of sweet sold to a customer = $\$$4

In the given problem,

Number of wooden blocks needed for 20 boxes = y = 100

Number of boxes = x = 20

Number of wooden blocks needed for a box = k

The direct variation formula is,

y = k * x

100 = k * 20

k = $\frac{100}{20}$

k = 5

Number of wooden blocks needed for a box = 5

In the given problem,

Amount of sweet sold to 5 customers = y = $\$$20

Number of Customers = x = 5

Amount of sweet sold to a customer = k

The direct variation formula is,

y = k * x

20 = k * 5

k = $\frac{20}{5}$

k = 4

Amount of sweet sold to a customer = $\$$4