USING RATIOS TO DIVIDE QUANTITIES WORD PROBLEMS

Problem 1 :

To make standard concrete, gravel, sand and cement are mixed in the ratio 5 : 3 : 1. I wish to make 18 tonnes of concrete. How much gravel, sand and cement must I purchase?

Solution :

Total parts  =  5 + 3 + 1

  =  9 parts

Quantity of concrete  =  18 tones

Quantity of gravel  =  5/9 of 18

=  (5/9) ⋅ 18

=  10 tonnes of gravel

Quantity of sand  =  3/9 of 18

=  (3/9) ⋅ 18

=  6 tonnes of sand

Quantity of cement  =  1/9 of 18

=  (1/9) ⋅ 18

=  2 tonnes of cement

Problem 2 :

My fortune of $810, 000 is to be divided in the ratio 4 : 3 : 2. How much does each person receive?

Solution :

Let X, Y and Z be three persons.

Total number of parts  =  4 + 3 + 2

=  9 parts

Amount received by X  =  4/9 of 810 000

=  (4/9) ⋅ 810 000

=  360000

Amount received by Y  =  3/9 of 810 000

=  (3/9) ⋅ 810 000

=  270000

Amount received by Z  =  2/9 of 810 000

=  (2/9) ⋅ 810 000

=  180000

Problem 3 :

An alloy is made from copper, zinc and tin in the ratio 17 : 2 : 1. How much zinc is required to make 10 tonnes of the alloy?

Solution :

Total number of parts  =  17 + 2 + 1

=  20 parts

Quantity of Zinc required  =  (2/20) of 10 tonnes

=  (2/20) ⋅ 10

=  1 tonne

Problem 4 :

Joe and Bob share the cost of a video game in the ratio 3 : 7.

a) What fraction does each pay?

b)  If the game costs $35, how much does each pay?

c)  If Joe pays $12, how much does Bob pay?

d)  If Bob pays $42, what is the price of the video game

Solution :

Total parts  =  3 + 7

  =  10 parts

(a)  Joe will pay 3/10 and Bob will pay 7/10.

(b)  Cost of game  =  $35

Joe has to pay  =  (3/10) of 35

=  (3/10) ⋅ 35

=  $10.5

Bob has to pay  =  (7/10) of 35

=  (7/10) ⋅ 35

=  $24.5

c)  Amount paid by Joe  =  3x

3x  =  12

x  =  4

Amount paid by Bob  =  7x

=  7(4) 

=  $28

d) 7x  =  42

x  =  6

Price of video game  =  10x

=  10(6)

=  60

Problem 5 :

A recipe calls for 1 cup of milk for every 2 1/2 cups of flour to make a cake that would feed 6 persons. How many cups of both flour and milk will be needed to make a similar cake for 8 people ?

Solution :

Ratio between milk to flour to number of people feed

= 1 : 2  1/2 : 6

To make a cake that serves for 6 persons, we need to mix milk and flour.

The part of milk and flour = 1 + 2  1/2

= 1 + 5/2

= 7/2

Ratio between milk with flour and number of persons to be serve

= 7/2 : 6

= 7 : 12

Let x be the quantity of milk with flour and number of persons.

Comparing the ratios, we get

7 : 12 :: x : 8

7/12 = x/8

7(8) = 12x

x = 7(8)/12

x = 7(2)/3

= 14/3

= 4  2/3

So, the required cups of milk with flour is 4  2/3.

Problem 6 :

In a school, the ratio of the number of large classrooms to small classrooms is 3:4. If the number of small rooms is 20, then find the number of large rooms

Solution :

Ratio between number of large class room to small class rooms = 3 : 4

Number of small class rooms = 4x

4x = 20

x = 20/4

x = 5

Number of small class rooms = 3x

= 3(5)

= 15

So, the required number of small class rooms is 15.

Problem 7 :

The students of a school belong to different religious backgrounds. The number of Hindu students is 288, the number of Muslim students is 252, the number of Sikh students is 144 and the number of Christian students is 72. Find the ratio of

(a) the number of Hindu students to the number of Christian students.

(b) the number of Muslim students to the total number of students.

Solution :

Number of Hindu students = 288

Number of muslim students = 252

Number Sikh students = 144

Number of Christin students =  72

Total number of students = 288 + 252 + 144 + 72

= 756

a) Ratio between number of Hindu to Christian students 

= 288 : 72

= 4 : 1

So, the ratio between number of Hindu to Christian student is 4 : 1

b) Ratio between number of Muslim students to the total number of students.

= 252 : 756

= 1 : 3

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