INVERSE RATIO WORKSHEET

Question 1 :

Find the inverse ratio of 11 : 15.

Question 2 :

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

Question 3 :

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

Question 4 :

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

Question 5 :

If x : y and 5 : 4 are inverse to each other find the value of x in terms of y.

Question 6 :

There are two number of which the first one is 24. If the inverse ratio of the two numbers is 5 : 8, find the second number.

1. Answer :

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

Inverse ratio of 11 : 15 is

15 : 11

2. Answer :

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

3. Answer :

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.

4. Answer :

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

5. Answer :

Since x : y and 5 : 4 are inverse to each other, their product is equal to 1.

(x : y)(5 : 4) = 1

(x/y)(5/4) = 1

5x/4y = 1

Multiply both sides by 4y.

5x = 4y

Divide both sides by 5.

x = 4y/5

6. Answer :

Let y be the second number.

The two ratios 24 : y and 5 : 8 are inverse to each other.

(24 : y)(5 : 8) = 1

(24/y)(5/8) = 1

120/8y = 1

15/y = 1

Multiply both sides by y.

15 = y

So, the second number is 15.

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