EXPRESS THE GIVEN RATIO IN SIMPLEST FORM WORD PROBLEMS

Write the following comparisons as ratios in simplest form. Compare the First quantity mentioned with the second quantity mentioned.

Example 1 :

A shirt costing €64 to another costing €32

Solution :

Cost of shirts :

=  64 : 32

Highest Common factor of 64 and 32 is 32

=  (64/32) : (32/32)

=  2 : 1

So, the simplest form is 2 : 1

Example 2 :

A rock melon of mass 3 kg to a watermelon of mass 9 kg

Solution :

Mass of rock melon : Mass of water melon

=  3  :  9

Highest Common factor of 3 and 9 is 3

=  (3/3) : (9/3)

=  1 : 3

So, the simplest form is 1 : 3

Example 3 :

The height of a 1.5m shrub to the height of a 6m tree

Solution :

Given height of a 1.5m shrub and height of a 6m tree

So, shrub to tree  =  1.5 : 6

Multiplying both by 10, we get

=  15 : 60

Highest Common factor of 15 and 60 is 15

=  (15/15) : (60/15)

=  1 : 4

So, the simplest form is 1 : 4

Example 4 :

A wetsuit costing $175 to a wetsuit costing $250

Solution :

Cost of wet suit :

=  175 : 250

Highest Common factor of 175 and 250 is 25

=  (175/25) : (250/25)

=  7 : 10

So, the simplest form is 7 : 10

Example 5 :

The top speed of a car which is 150 km h^-1 to the top speed of a formula. One car which is 350 km h^-1

Solution :

Ratio of speed :

=  150 : 350

Highest Common factor of 150 and 350 is 50

=  (150/50) : (350/50)

=  3 : 7

So, the simplest form is 3 : 7

Example 6 :

A log of length 4m to a stick of length 10cm

Solution :

As both the measurements are in different units, first make their units same.

1m  =  100 cm

4m  =  400 cm

Highest Common factor of 400 and 10 is 10

=  (400/10) : (10/10)

=  40 : 1

So, the simplest form is 40 : 1

Example 7 :

The height of an insect which is 2mm to the height of a rat which is 10 cm

Solution :

As both the measurements are in different units, first make their units same.

2mm  =  0.2cm

So, insect to rat  =  0.2 : 10

Multiplying both by 10, we get

=  2 : 100

Highest Common factor of 2 and 100 is 2

=  (2/2) : (100/2)

=  1 : 50

So, the simplest form is 1 : 50

Example 8 :

(a)  Shorter side of A : Shorter side of B

(b)  longer side of A : longer side of B

(c)  Area of A : Area of B

Solution :

(a)  Shorter side of A : Shorter side of B

=  3 : 6

=  1 : 2

So, the ratio is 1 : 2

(b)  longer side of A : longer side of B

=  5 : 10

=  1 : 2

So, the ratio is 1 : 2

(c)  Area of A : Area of B

Area of Rectangle A  = 5(3)

=  15 cm²

Area of Rectangle B  = 10 × 6

=  60cm²

Area of A : Area of B  =  15 : 60

=  1 : 4

Example 9 :

IF 2/3 of the workers in an office are non smokers, what is the ratio of smokers to nonsmokers ?

a)  2 : 5   b)  1 : 2   c)  3 : 5    d) 2 : 3

Solution :

From the given fraction, we understand that

2 x = non smoker

3x = total number of workers in the office

Smokers = 3x - 2x

= 1x

Ratio between smokers to non smokers 

1x : 2x

= 1 : 2

So, option b is correct.

Example 10 :

If 80% of the applicants to a program were rejected, what is the ratio of the number accepted to the number rejected ?

a)  1/5   b)  1/4    c)  2/5   d)  4/5

Solution :

Total number of applicants to be 100%

80% of the applicants are rejected, then 20% of the applicants can be selected.

Ratio between accepted to rejected = 20 : 80

= 20/80

= 2/8

= 1/4

So, option b is correct.

Example 11 :

If a : b = 3 : 5 and a : c = 5 : 7, what is the ratio of b : c?

a)  21 : 35   b)  21 : 25    c)  25 : 21    d)  35 : 21

Solution :

a : b = 3 : 5 and a : c = 5 : 7

Multiplying the first ratio by 5 and second ratio by 3, we get

a : b = 15 : 25

a : c = 15 : 21

b : a = 25 : 15

b/a = 25/15

c : a = 21:15

c/a = 21/15

b/a = c/a => 25/15 = 21/15

b/c = 25/21

b : c = 25 : 21

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