PROPORTION WORD PROBLEMS WITH ANSWERS

Problem 1 :

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.

Solution :

(a)  Let x be the number of doctors in the team.

According to the information, the number of engineers and doctors are in the ratio 2 : 5.

2 : 5 = 18 : x

Product of extremes = Product of means

2x = 5(18)

x = 5(18)/2

x = 5(9)

x = 45

So, the number of doctors in that team is 45.

b) Let y be the number of engineers in that team.

2 : 5 = y : 65

2(65) = 5y

y = 2(65)/5

y = 2(13)

y = 26

So, the number of engineers in that team is 26.

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

Problem 2 :

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°.

Solution :

Let 3x be the larger angle and x be the smaller angle.

(a)  If x = 18 (Smaller angle).

3x = 3(18)

= 54

If smaller angle is 18, then larger angle is 54°.

b) smaller angle if the larger is 63°.

Larger angle (3y) = 63°

y = 63/3

y = 21

So, the smaller angle is 21°.

Problem 3 :

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

Solution :

Ratio of teachers to students = 1 : 15.

Number of teachers = x and students = 15x

Total number of students = 675.

15x = 675

x = 675/15

x = 45

So, number of teachers is 45.

Problem 4 :

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

Solution :

Cost price of MP3 = $240 and selling price = $270.

Sot price : selling price = 240 : 270

= 240/270

= 8/9

= 8 : 9

So, the cost price and selling price are in the ratio 8 : 9.

Problem 5 :

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.

Solution :

Ratio of speeds of boat and car = 2 : 7.

2x = Speed of Boat and 7x = Speed of car

Speed of boat = 30 km per hour

2x = 30

x = 15

Speed of car = 7(15)

= 105 km/hr

Problem 6 :

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.

c) Find the ratio of the total number of animals to the number of cattle.

Solution :

8x = Number of sheep and 3x = number of cattle

(a) Number of cattle = 180

3x = 180

x = 180/3

x = 60

Number of sheep = 8(60) = 480.

b) Total number of animal = 3x + 8x.

= 11x

= 11(60)

= 660

Number of sheep : Number of animal

= 480 : 660

= 480/660

= 8 : 11

c) Total number of cattle = 660.

660 : 180

By simplifying, we get

= 66 : 18

= 66/6 : 18/6

= 11 : 3

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