INVERSE RATIO

Example 1 :

Find the inverse ratio of 11 : 15.

Solution :

To get inverse ratio of 11 : 15, switch its terms.

Inverse ratio of 11 : 15 is

15 : 11

Example 2 :

If the two ratios x : 5 and 10 : 13 are inverse to each other, find the value of x.

Solution :

If two ratios are inverse to each other, their product is equal to 1.

(x : 5)(10 : 13) = 1

(x/5)(10/13) = 1

10x/65 = 1

Multiply both sides by 65.

10x = 65

Divide both sides by 10.

x = 65/10

x = 13/2

x = 6.5

Example 3 :

The ratio of the quantities is 5 : 7. If the second term of of its inverse ratio is 10, find the first term.

Solution :

Let x be the first term of the inverse ratio of 5 : 7.

The two ratios 5 : 7 and x : 10 are inverse to each other.

So, their product is equal to 1.

(5 : 7)(x : 10) = 1

(5/7)(x/10) = 1

5x/70 = 1

 x/14 = 1

Multiply both sides by 14.

x = 14

14 is the first term of the inverse ratio of 5 : 7.

Example 4 :

Given that y = 2x - 3, if y : x and 2 : 3 are inverse to each other find the value of x.

Solution :

Since y : x and 2 : 3 are inverse to each other, their product is equal to 1.

(y : x)(2 : 3) = 1

(y/x)(2/3) = 1

2y/3x = 1

Multiply both sides by 3x.

2y = 3x

Substitute y = 2x - 3.

2(2x - 3) = 3x

4x - 6 = 3x

Subtract 3x from both sides.

x - 6 = 0

Add 6 to both sides.

x = 6

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