Ratio

Ratio is the numerical relation of one quantity to another of the same kind. To find the ratio of 2 m 25 cm to 75 cm, we first change 2 m 25 cm into cm, which equals 225 cm. Now, we have to find 225 cm to 75 cm

ratio is

= 3 : 1

We can write the above ratio as

(i) 3 : 1 or (ii) or (iii) the ratio 3 to 1 or (iv) 3

(i) The ratio should be expressed in simplified form.

(ii) Ratio has no units

If the ratio of two similar quantities is a : b, then the first quantity 'a' is called the antecedent; the second quantity 'b' is called the consequent.

Find the ratio of 2 hours 30 minutes to 45 minutes.

2 hours 30 minutes = 150 minutes

ratio is 150 minutes : 45 minutes or 10:3

Ans: 10 : 3

Simplify the ratio

can be rewritten as or

9 : 5

Ans: 9 : 5

Compounded Ratio

When two or more ratios are multiplied with each other, the resultant simplified ratio is called the compounded ratio.

Let a : b and c : d be two given ratios, then the compounded ratio is

= ac : bd.

Duplicate ratio

The ratio a²: b², obtained by compounding the ratio a : b with itself is called the duplicate ratio, .

For example, the duplicate ratio of 4 : 9 is 4² : 9²

= 16 : 81

Triplicate Ratio

The ratio a³ : b³ obtained by compounding the ratio a : b with itself three times, = is called the triplicate ratio.

For example, the triplicate ratio of 4 : 9 is 4³ : 9³

or 64 : 729

Sub-duplicate Ratio:

The ratio obtained by taking the square root of the given ratio a:b is called the sub-duplicate ratio. is the sub-duplicate ratio of a : b.

For example, the sub-duplicate ratio of 4 : 9 is

or 2 : 3

Sub-triplicate Ratio:

The ratio obtained by taking the cube root of the given ratio a : b is called sub-triplicate ratio. is sub-triplicate ratio of a : b.

For example the sub-triplicate ratio of 8a³ : 27b⁶ is

or 2a : 3b².

Find the compounded ratio of the duplicate ratio of ; sub-triplicate ratio of 9261 : 729 and reciprocal ratio of 16 : 15.

Duplicate ratio of

= 12 : 7

Sub-triplicate ratio of 9261 : 729 =

= 21 : 9

Reciprocal ratio of 16 : 15 = 15 : 16

Compounded ratio

= 15 : 4

Ans: 15 : 4

Find the compounded ratio of the following:

Sub-duplicate ratio of x⁴ y⁶ : 81a⁴,

Triplicate ratio of 3a : 2xy², and

Sub-triplicate ratio of 64x³y⁹ : 343 b³.

Sub-duplicate ratio of x⁴y⁶ : 81a⁴

= x² y³ : 9a²

Triplicate ratio of 3a : 2xy² = (3a)³ : (2xy²)³

= 27a³ : 8x³ y⁶

Sub-triplicate ratio of 64x³y⁹ : 343b³

= 4xy³ : 7b

Compounded ratio

= 3a : 14 b

Ans: 3a : 14b.