# 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 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