Worksheet on Types of Ratios

Practice the questions given in the worksheet on types of ratios that is compound ratio, duplicate ratio, triplicate ratio, subduplicate ratio, subduplicate ratio and reciprocal ratio.

1. Find the compound ratio of the following ratios.

(i) 3 : 5 and 8 : 15

(ii) a : b and b : c

(iii) (x\(^{2}\) - y\(^{2}\)) : (x\(^{2}\) + y\(^{2}\)) and (x\(^{4}\) - y\(^{4}\)) : (x + y)\(^{4}\)

2. Find the compound ratio of each of the following three ratios.

(i) 2 : 3, 9 : 14 and 14 : 27

(ii) x : y, y : z and z : w

(iii) 2a : 3b, mn : x\(^{2}\) and x : n

(iv) 3 : 5, 7 : 9 and 15 : 28

(v) √2 : 1, 3 : √5 and √20 : 9

(vi) (a + x) : (a - x), (a\(^{2}\) + x\(^{2}\)) : (a + x)\(^{2}\) and (a\(^{2}\) - x\(^{2}\))\(^{2}\) : (a\(^{4}\) - x\(^{4}\))

3. Find the duplicate ratio of each of the following ratios.

(i) 3 : 4

(ii) √2 : √3

(iii) 3√3 : 2√5

(iv) 3a : 4b

(v) \(\sqrt{9a}\) : 4√a

4. Find the triplicate ratio of

(i) 1 : 3

(ii) \(\frac{x}{2}\) : \(\sqrt[3]{x}\)

(iii) \(\frac{m}{2}\) : \(\frac{n}{3}\)

(iv) \(\sqrt[3]{9}\) : √8

5. Find the subduplicate ratio of

(i) 9 : 16

(ii) x\(^{4}\) : y\(^{2}\)

(iii) (x - y)\(^{4}\) : (x + y)\(^{6}\)

(iv) \(\frac{1}{4}\) : \(\frac{1}{36}\)

6. Find the subtriplicate ratio of

(i) 64 : 27

(ii) a\(^{3}\) : 8b\(^{3}\)

(iii) x\(^{3}\) : 125y\(^{3}\)

(iv) 64 : 729

7. Find the reciprocal ratio of

(i) 5 : 8

(ii) \(\frac{1}{72}\) :  \(\frac{1}{27}\)

(iii) \(\frac{x}{3}\) : \(\frac{y}{7}\)

(iv) a\(^{2}\) : b\(^{2}\)

Answers:

Answers for the worksheet on types of ratios are given below.

1. (i) 8 : 25

(ii) a : c

(iii) (x - y)\(^{2}\) : (x + y)\(^{2}\)

2. (i) 2 : 9

(ii) x : w

(iii) 2am : 3bx

(iv) 1 : 4

(v) 2√2 : 3

(vi) 1 : 1

3. (i) 9 : 16

(ii) 2 : 3

(iii)  27 : 20

(iv) 9a\(^{2}\) : 16b\(^{2}\)

(v) 9 : 16

4. (i) 1 : 27

(ii) x\(^{2}\) : 8

(iii) 27m\(^{3}\) : 8n\(^{3}\)

(iv) 9 : 16√2

5. (i) 3 : 4

(ii) x\(^{2}\) : y

(iii) (x - y)\(^{2}\) : (x + y)\(^{3}\)

(iv) 3 : 1

6. (i) 4 : 3

(ii) a : 2b

(iii) x : 5y

(iv) 4 : 9

7. (i) 8 : 5

(ii) 8 : 3

(iii) 3y : 7x

(iv) b\(^{2}\) : a\(^{2}\)

● Ratio and proportion

• Basic Concept of Ratios
• Important Properties of Ratios
• Ratio in Lowest Term
  
• Types of Ratios
• Comparing Ratios
• Arranging Ratios
  
• Dividing into a Given Ratio
  
• Divide a Number into Three Parts in a Given Ratio
• Dividing a Quantity into Three Parts in a Given Ratio
  
• Problems on Ratio
  
• Worksheet on Ratio in Lowest Term
  
• Worksheet on Types of Ratios
  
• Worksheet on Comparison on Ratios
• Worksheet on Ratio of Two or More Quantities
  
• Worksheet on Dividing a Quantity in a Given Ratio
• Word Problems on Ratio
  
• Proportion
  
• Definition of Continued Proportion
  
• Mean and Third Proportional
  
• Word Problems on Proportion
  
• Worksheet on Proportion and Continued Proportion
  
• Worksheet on Mean Proportional
  
• Properties of Ratio and Proportion

10th Grade Math

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