FIND THE MISSING NUMBER IN RATIO AND PROPORTION

A proportion is a statement that two quantities are equal.

If two ratios are equal, then

Example 1 :

Find the missing numbers in the following proportions :

(i) Answer :

Let x be the missing term.

3 : 4 = 6 : x 

If two ratios are equal, then

Product of means = Product of extremes

3 ⋅ x = 4 ⋅ 6

3x = 24

x = 8

(ii) Answer :

Let x be the missing term.

5 : 8 = x : 40

If two ratios are equal, then

Product of means = Product of extremes

5 ⋅ 40 = 8 ⋅ x

200 = 8x

x = 25

(iii) Answer :

Let x be the missing term.

7 : 21 = x : 33

If two ratios are equal, then

Product of means = Product of extremes

7 ⋅ 33 = 21 ⋅ x

231 = 21x

x = 11

(iv) Answer :

Let x be the missing term.

5 : 100 = x : 40

If two ratios are equal, then

Product of means = Product of extremes

5 ⋅ 40 = 100 ⋅ x

200 = 100x

x = 2

(v) Answer :

Let x be the missing term.

2 : 5 = x : 15

If two ratios are equal, then

Product of means = Product of extremes

5 ⋅ 40 = 100 ⋅ x

200 = 100x

x = 2

Example 2 :

A disaster relief team consists of engineers and doctors in the ratio of 2 : 5.

a) If there are 18 engineers, find the number of doctors.

b) If there are 65 doctors, find the number of engineers.

Answer :

Given :

Ratio of engineers to Doctors

= 2 : 5

(a) Ratio between engineers to doctors, when engineers are 18.

Let x be the number of doctors.

2 : 5 = 18 : x

2x = 5(18)

x = 45

(b) Ratio between engineers to doctors, when doctors are 65.

Let y be the number of engineers.

2 : 5 = y : 65

2(65) = 5y

y = 2(65)/5

y = 26

Example 3 :

The ratio of two angles in a triangle is 3 : 1. Find the :

a) larger angle if the smaller is 18.

b) smaller angle if the larger is 63.

Answer :

(a) Let x be the larger angle.

Ratio of larger to smaller angle = 3 : 1.

3 : 1 = x : 18

Product of means = Product of extremes.

3(18) = 1(x)

x = 54

So, the larger angle is 54.

(b)  Let y be the smaller angle.

3 : 1 = 63 : y

3y = 63

y = 21

So, the smaller angle is 21.

Example 4 :

The ratio of teachers to students in a school is 1 : 15. If there are 675 students, how many teachers are there?

Answer :

Let x be the number of teachers.

Ratio between teachers to students = 1 : 15.

Number of students = 675.

1 : 15 = x : 675

Product of means = Product of extremes

1(675) = 15x

x = 675/15

x = 45

So, the number of teachers are 45.

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