**Proportion Problems with Answers:** Usually a proportion is nothing but a mathematical method that is important for evaluating problems based on fractions. Through this article, the 6th Grade Math students can gain more knowledge about the different proportion problems by utilizing the symbol “::” otherwise “=” in between the given variables.

In maths, proportion is nothing but an equation that is used to find that the given two ratios are equivalent to each other. It’s formula is x:y :: m:n or (x/y) = (m/n). Here word problems on proportion are solved by using the proportion formula and cross-product Rule.

**Also, Refer**

- Concept of Proportion
- Worksheet on Proportions
- Properties of Proportion
- Multiple Choice Questions on Ratio and Proportion
- Continued Proportion
- What is Ratio and Proportion
- Practice Test on Ratio and Proportion

## Problems on Proportion with the Solutions

**1.** **Calculate the value of y , when 12 / 4 : x = 2 / 5 : 7 / 8**

## Solution:

Given numbers are 12 / 4 , x , 2 / 5 and 7 / 8.

To know the value of x implement the cross-product rule (12 /4). (7 / 8 ) = (x) .( 2/ 5 )

(84 / 32) = 2x / 5

(84 / 32) .(5 /2) = x

420 / 64 = x

Hence the Resultant value of x = 6.5

**2. What is the fourth proportional for the given numbers 2, 7, 4.**

## Solution:

Given numbers are 2,7,4

To know the fourth proportional value, Let the number y i.e. 2: 7 = 4: x

try to implement the cross-product rule 2 x y = 4 x 7

2y = 28

y = 28/ 7

y = 4 which is the Resultant value nothing but the Fourth proportional value.

**3. When v : x = y : z = 4 : 7, calculate the values of vz : xy and v +y v + y and x + z?**

## Solution:

For a specified proportion of v: x and y: z, implement the cross product Rule as shown below

vz = xy

Divide with bc on L.H.S and R.H.S it is obtained as vz: xy = 1: 1

and v : x and y : z = 4 : 7. Assume it as Equation (1).

Now implement the addendo property v : x = y : z = (v+ x) : (y +z) Assume it as Equation (2)

By Equating both the Equations , i.e. (v+ x) : (y +z) = 4 : 7

**4. Does the numbers 4 : 12 :: 6 : 2 in proportion**

## Solution:

Given that 4, 12, 6, and 2 are four numbers, To check whether the given numbers are in proportion, we simply the cross product rule(product of mean terms = product of extreme terms) as shown below.

4 : 12 :: 6 : 2

4 x 2 = 6 x 12**
**8 = 72

Hence they are not in Proportion.

**5. Calculate the third proportional of 8 and 6**

## Solution:

Given that 8 and 6 are the two numbers and the third number is unknown, assume the proportional number be y. Then the three numbers are proportional. i.e. which indicates as 8 : 6 = 6 : y**
**By implementing the cross product rule, the product of Extreme terms = product of mean terms

8 x y = 6 x 6

8y = 36

y = 36 /8

y = 4.5

**6. Kumar studies 8 mathematics books in 15 hours. Imagining the overall books containing a similar length, calculate the number of hours for studying the 12 Books?**

## Solution:

Given that 8 mathematics books in 15 hours. Let the number of hours taken to study the 12 Books be y. To calculate the value of y implement the proportion formula as shown below

8 / 15 = 12 / y

implementing the cross product rule, it is obtained as 8y = 12 x 15

8y = 180

y = 180/ 8

y = 22.5 hours for studying the 12 mathematics books.

**7. Suppose p is directly proportional to r when r = 3 and p = 6, calculate the value of r when p = 12**

## Solution:

Given problem is an example for Direction proportion(p ∝ r) By implementing it, we get as below.

3 / 6 = r / 12

By Cross multiplying , 3 x 12 = r x 6

36 = r x 6

r = 36 / 6

r = 6 is the Resultant value.

**8. Suppose a bike travels 130 miles in 4 hours. How many miles that the bike travels in 6 hours?**

## Solution:

bike travels in 4 hours = 130 miles

bike travels in 6 hours = ? .Let it be the x miles

130 miles / 4 = x miles / 6hours

x = (130 / 4) . 6

x = 195 miles. It is the Resultant value that a bike travels in 6 hours.

**9. When s is inversely proportional to r when r = 4 when s = 2. what is the value of r if s = 9.**

## Solution:

Given problem is an example for Indirect proportion. (s ∝ 1/ r). By implementing it, we get as below

2 x 4 = 9 x r

r = 8 / 9