If you are seeking help on the concept of Ratio and Proportion you can always make use of Worked out Problems on Ratio and Proportion. All the Problems are explained with straightforward description making it easy for you to understand the concept. Solve different problems on Ratio and Proportion available here firstly on your own and cross-check your solutions.

You can find Ratio and Proportion Questions related to Simplification of Ratios, Comparison of Ratios, Arranging Ratios in Ascending Order, Descending Order, Word Problems on Ratio and Proportion, etc. Sample Problems on Ratio and Proportion will help you get a good grip on the concept and its fundamentals too in no time.

## Ratio and Proportion Problems and Solutions

**1. Two numbers are in the ratio 4 : 5. If the sum of numbers is 72, find the numbers?**

Solution:

Let the numbers be 4x and 5x

Since Sum of the Numbers is 72 we have the equation as such

4x+5x = 72

9x= 72

x = 72/9

= 8

Substitute the value of x to obtain the numbers

4x = 4*8 32

5x = 5*8 = 40

Therefore, the Numbers are 32 and 40.

**2. If x : y = 3 : 2, find the value of (2x + 4y) : (x + 5y)?**

Solution:

We know x:y = 3:2

we can rewrite it as

x/y = 3/2

Given equation (2x + 4y) : (x + 5y)

we can rewrite it as

(2x + 4y)/(x + 5y)

Dividing Numerator and Denominator with y we have the equation as follows

= (2(x/y)+4(y/y))/((x/y)+5(y/y))

Since we know the value of x/y substitute it in the above equation

= (2(1/2)+4(1))/((1/2)+5(1))

= (1+4)/(1/2+5)

= 5/(11/2)

= 10/11

Therefore, value of (2x + 4y) : (x + 5y) is 10/11.

**3. The average age of three boys is 36 years and their ages are in the proportion 5 : 6 : 7. Find the age of the youngest boy?**

Solution:

From the ratio 5:6:7, the ages of boys are 5x, 6x, 7x

Given Average Age of Boys = 36

5x+6x+7x = 36

18x = 36

x = 2

Age of Youngest Boy = 5x

= 5*2

= 10 years

Therefore, the Age of the Youngest Boy is 10 Years.

**4. If 3A = 4B = 5C, find A : B : C?**

Solution:

Let us assume a constant k

3A=4B=5C = k

equating them we have

3A= k, 4B = k, 5C = k

A = k/3, B = k/4, C = k/5…….(1)

Finding LCM for the obtained values 3, 4, 5

LCM(3, 4, 5) = 60

Multiplying with 60 the eqn (1) we get the Ratio as Follows

Ratio of A:B:C is 20:15:12

**5. What must be added to each term of the ratio 3 : 2, so that it may become equal to 5 : 4?**

Solution:

Let the Number to be added be x then (3+x):(2+x) = 5:4

(3+x)/(2+x) = 5/4

(3+x)4 = 5(2+x)

12+4x= 10+5x

12-10 = 5x-4x

x =2

To make the ratio 3:2 to 4:5 you need to add 2.

**6. The length of the ribbon was originally 33 cm. It was reduced in the ratio 3:2. What is its length now?**

Solution:

Length of Ribbon = 33 cm

Let the Original Length be 3x

Reduced Length be 2x

But 3x = 33 cm

x = 33 cm/3

= 11 cm

Reduced Length = 2x

= 2*11

= 22 cm

Therefore, the Length of the Ribbon is 22 Cm.

**7. The ratio of the number of boys and girls is 5 : 3. If there are 15 girls in a class, find the number of boys in the class and the total number of students in the class?**

Solution:

Given Ratio of Boys to Girls is 5:3

There are 15 Girls in the Class

Boys/Girls = 5/3

Boys/15 = 5/3

Boys = (5*15)/3

= 25

Number of Students in Class = Boys +Girls

= 25+15

= 40

Therefore, there are 25 Boys and 40 Students in the Class.

**8. Find the third proportional of 10 and 20?**

Solution:

Let us consider the Third Proportional of 10 and 20 be x

10, 20, and x are in Proportion

10:20 = 20:x

Product of Means = Product of Extremes

20*20 = 10*x

400 =10x

x = 400/10

= 40

Third Proportional of 10, 20 is 40

**9. The first, second, and third terms of the proportion are 40, 36, 35. Find the fourth term?**

Solution:

Let us consider the fourth term be x

40, 36, 35, x

Product of Means = Product of Extremes

36*35 = 40*x

x = (36*35)/40

= 31.5

Fourth Proportional of 40, 36, 35 is 31.5

**10. Arrange the following ratios in Ascending Order**

** 3:2, 4:3, 5 : 6, 1 : 4**

Solution:

Given Ratios are 3/2, 4/3, 5/6 and 1/4

Finding the LCM of 2, 3, 6, 4 we get 12

Express the given ratios in terms of common denominator we get

3/2 = (3*6/2*6) = 18/12

4/3 = (4*4/3*4) = 16/12

5/6 = (5*2/6*2) = 10/12

1/4 = (1*3/4*3) = 3/12

Clearly, 3/12<10/12<16/12<18/12

Therefore, 1:4 <5:6<4:3<3:2