Illustrative Examples

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Example 1:

Find the compounded ratio of

a) 5:14 and 7:15

b) a+b:a-b; (a²-b²):(a²+b²) and a²+b²:(a+b)²

Suggested answer:

a) The compounded ratio of 5:14 and 7:15 is

b)The compounded ratio of a+b:a-b; a²-b²:a²+b² and a²+b²:(a+b)² is (a+b) (a²-b²) (a²+b²) : (a-b) (a²+b²) (a+b)²

(a+b) (a+b) (a-b) : (a-b) (a+b) (a+b)

1:1

Example 2:

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

Suggested answer:

Example 3:

If 2x - y : 3x - 2y = 3:4, find x:y.

Suggested answer:

4(2x-y)=3(3x-2y)

8x-4y=9x-6y

6y-4y=9x-8x

2y=x

x:y=2:1

Example 4:

In the ratio 7:8, if the consequent is 40, what is the antecedent?

Suggested answer:

x=35

Antecedent=35.

Example 5:

If a:b = 5:8. Find the value of a²b+ab²:a³+b³.

Suggested answer:

Example 6:

Find

a) reciprocal ratio of 3:5

b) duplicate ratio of 2:3

c) triplicate ratio of 3:4

d) sub duplicate ratio of 25:16

e) sub triplicate ratio of 27:8

Suggested answer:

a) Reciprocal ratio of 3:5

b) Duplicate ratio of 2:3

=2²:3²=4:9

c) Triplicate ratio of 3:4

= 3³:4³

= 27:64

d) Sub duplicate ratio of 25:16

=5:4

e) Sub triplicate ratio of 27:8

= 3:2

Example 7:

If a:b=4:5, b:c=6:7, find a:c and a:b:c.

Suggested answer:

Hence a:c = 24:35

{a:b = 4:5} x 6

{b:c = 6:7} x 5

a:b = 24:30

b:c = 30:35 (To make b equal in both ratio)

Hence a:b:c = 24:30:35

Example 8:

Suggested answer:

12a+18 = 25a-190

25a-12a = 18+190

13a = 208

a = 16

Example 9:

Two numbers are in the ratio 3:4. If 8 is added to the numbers, the ratio becomes 5:6. Find the numbers.

Suggested answer:

6x+48 = 5y+40

y = 16

Example 10:

Divide Rs.256 in the ratio 7:9.

Suggested answer:

Let x be common to the ratio 7:9.

7x, 9x

7x+9x=256

16x=256

Hence, the parts are 7 x 16 = Rs.112

and 9 x 16 = Rs.144.