FIND MISSING NUMBERS IN PROPORTION WORKSHEET

Question 1 :

Find the missing numbers in the following proportions :

Question 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.

Question 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.

Question 4 :

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

Question 5 :

An MP3 player is bought for $240 and sold for $270. Find the ratio of the cost price to the selling price.

Question 6 :

The maximum speeds of a boat and a car are in the ratio 2 : 7. If the maximum speed of the boat is 30 km per hour, find the maximum speed of the car.

Question 7 :

A farmer has sheep and cattle in the ratio 8 : 3.

a) How many sheep has the farmer if he has 180 cattle?

b) Find the ratio of the number of sheep to the total number of animals.

1. Answer :

(i) :

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) :

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) :

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) :

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) :

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

2. 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

3. 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.

4. 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.

5. Answer :

Cost price : Selling price  =  240 : 270

=  240/270

=  8/9

So, the ratio between cost price to selling price  =  8 : 9.

6. Answer :

Ratio of maximum speeds of boat to car  =  2 : 7

Speed of boat  =  30

Let x be the speed of car.

2 : 7  =  30 : x

2x  =  7(30)

x  =  210/2

x  =  105 km

So, speed of car is 105 km.

7. Answer :

Ratio between sheep and cattle  =  8 : 3

Let x be the number of sheep when number of cattle are 180.

8 : 3  =  x : 180

8(180)  =  3x

x  =  180(8)/3

x  =  480

So, total number of sheep is 480.

(b)  Number of sheep  =  480

Total number of animal  =  Number of sheep + number of cattle

=  480+180

=  660

Ratio of number of sheep :  Number of animal

=  480 : 660

=  48 : 66

=  8 : 11

So, ratio between number of sheep to total number of animal is 8 : 11.

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