Practicing from Worksheet on Ratio and Proportion helps students to think more of the concept. Solve Ratio and Proportion Question and Answers available to score better grades in the exam. The Questions in this Worksheet are based on Expressing Ratios in their Simplest Form, Simplification of Ratios, Comparison of Ratios, Arranging Ratios in Ascending and Descending Order, Mean Proportional Between Numbers, etc.

Solve as many times as possible in order to be familiar with the types of Ratio and Proportion Questions. Answering the Problems over here helps you get a good grip on the entire concept. In addition, you will learn the tips and tricks on how to solve ratio and proportion problems using different methods. For better understanding, we even listed solutions for each and every problem making it easier for you to cross-check whether your answers are correct or not.

1. Express each of the following ratios in the simplest form

(a) 5.6 m to 28 cm

(b) 6 hours to a day

(c) 20 liters to 15 liters

(d) 170 : 240

## Solution:

(a) 5.6 m to 28 cm

1 m = 100cm

5.6 m = 5.6*100 = 560 cm

Ratio of 5.6m to 20 cm = 560 cm: 20 cm

= 140:5

= 28:1

(b) 6 hours to a day

In one day there are 24 hrs

6 hrs to a day = 6 hrs: 24 hrs

= 1 :4

(c) 20 liters to 15 liters

= 20 liters :15 liters

= 4:3

(d) 170 : 240

= 170/240

= 17/24

Therefore, ratio of 170:240 in its simplified form is 17/24

2. Simplify the following ratios

(a) 1/4 : 1/3 : 1/6

(b) 3.6 : 5.4

(c) 3²/₃ : 4¹/₂

## Solution:

(a) 1/4 : 1/3 : 1/6

LCM of 4, 3, 6 is 12

Expressing them in terms of a least common factor we have

1/4 = 3*3/4*3 = 9/12

1/3 = 1*4/3*4 = 4/12

1/6 = 1*2/6*2 = 2/12

Therefore 1/4:1/3:1/6 in simplified form is 9:4:2

(b) 3.6 : 5.4

Simplifying it we get the ratio as under

Dividing with GCD(3.6, 5.4) i.e. 0.9 we get the simplified form

= (3.6/0.9):(5.4/0.9)

= 4:6

(c) 3²/₃ : 4¹/₂

= 11/3:9/2

LCM of (3, 2) is 6

Expressing the given ratio in terms of LCM we get the equation as follows

11/3 = 11*2/3*2 = 22/6

9/2 = 9*3/2*3 = 27/6

Therefore, ratio 3²/₃ : 4¹/₂ in simplified form is 22:27

3. Compare the following ratios

(a) 5 : 2 and 4 : 3

(b) 1/3 : 1/5 and 1/5 ∶ 1/6

## Solution:

(a) 5 : 2 and 4 : 3

Express the given ratio as fraction we get

5:2 = 5/2

4:3 = 4/3

Find the LCM(2, 3) i.e. 6

Making the denominator equal to 6 we get

5/2 = 5*3/2*3 = 15/6

4/3 = 4*2/3*2 = 8/6

5:2 > 4:3

(b) 1/3: 1/5 and 1/5 ∶ 1/6

1/3:1/5

Finding LCM of 3, 5 we get the LCM as 15

Expressing the ratios given in terms of the LCM as a common denominator

1/3 = 1*5/3*5

= 5/15

1/5 = 1*3/5*3 = 3/15

thus it becomes 5:3

1/5 ∶ 1/6

Finding LCM of 5, 6 we get the LCM as 30

Expressing the ratios given in terms of the LCM as Common Denominator

1/5 = 1*6/5*6 = 6/30

1/6 = 1*5/6*5 = 5/30

Therefore, it becomes 6:5

Therefore, 1/3: 1/5 < 1/5 ∶ 1/6

4. In the ratio 3 : 5, the consequent is 20. Find the antecedent?

## Solution:

Let the Antecedent and Consequent be 3x and 5x

We know Consequent = 20

5x =20

x= 20/5

= 4

Antecedent = 3x

= 3*4

= 12

Therefore, Antecedent is 12.

5. Divide 2000 among A, B, C in the ratio 2 : 3 : 5?

## Solution:

Let the numbers be 2x, 3x, 5x

Sum = 2000

2x+3x+5x = 2000

10x = 2000

x = 2000/10

x = 200

Since the sum is to be split among A, B, C in the ratio of 2:3:5

we get A’s Share = 2x

B’s Share = 3x

C’s Share = 5x

A’s Share = 2*200

= 400

B’s Share = 3*200

= 600

C’s Share = 5*200

= 1000

Therefore, A, B, C’s Share in the amount of 2000 are 400, 600, 1000 respectively.

6. Determine whether the ratios form a Proportion or not

(a) 50 cm : 1 m = $80 : $160

(b) 200 ml : 2.5 l = $4 : $20

## Solution:

(a) 50 cm : 1 m = $80 : $160

50 cm: 1 m

We know 1m = 100 cm

= 50 cm: 100 cm

= 1:2

$80 : $160

= 1:2

Since both the ratios are equal they are said to be in Proportion

(b)200 ml : 2.5 l = $4 : $20

1 liter = 1000 ml

2.5 l = 2.5*1000

= 2500

200 ml: 2500 ml

= 2:25

$4:$20

= 1:5

Since both the ratios aren’t equal given values doesn’t form a Proportion.

7. Find the value of x in each of the following

(a) 4, 5, x, 48

(b) 7, 21, 30, x

(c) x, 28, 24, 4

## Solution:

(a) 4, 5, x, 48

We know Product of Means = Product of Extremes

4*48 = 5*x

5x = 192

x = 192/5

(b) 7, 21, 30, x

We know Product of Means = Product of Extremes

7*x = 21*30

x = (21*30)/7

= 90

(c) x, 28, 24, 4

We know Product of Means = Product of Extremes

x*4 = 28*24

x = (28*24)/4

= 168

8. Find the fourth proportional to 54, 27, 18, x

## Solution:

Product of Extremes = Product of Means

54*x = 27*18

x = (27*18)/54

= 9

9. Find the third proportional to

(a) 9, 6, x

(b) 6, 12, x

## Solution:

To find third proportional we write the expression as

9:6 = 6:x

9*x = 6*6

x = 36/9

= 4

(b) 6, 12, x

6:12 = 12:x

6*x = 12*12

x = 144/6

x= 24

10. Find the mean proportional between

(a) 5 and 20

(b) 1.6 and 0.4

## Solution:

Mean Proportional between two numbers is defined as the square root of the product of two numbers

(a) 5 and 20

= √(5*20)

=√100

= 10

Mean Proportional of 5 and 20 is 10

(b) 1.6 and 0.4

Mean Proportional between two numbers is defined as the square root of the product of two numbers

= √(1.6*0.4)

= v6.4

= 0.8

Mean Proportional of 1.6 and 0.4 is 0.8