RATIO AND PROPORTION PROBLEMS AND SOLUTIONS

Problem 1 :

The length and width of a rectangle is in the ratio 3 : 5. If its perimeter is 48 cm, find its length and width.

Solution :

From the given ratio, we have

length = 3x and width  =  5x

Perimeter = 48

2(l + w) = 48

2(3x + 5x) = 48

8x = 24

x = 3

Therefore,

length = 3(3) = 9 cm

width = 5(3) = 15 cm

Problem 2 :

If $1000 is divided among the three people in the following ratio

2 : 3 : 5

Find the share of each.

Solution :

From the given ratio,

share of the first person = 2x

share of the second person = 3x

share of the third person = 5x

Total Amount = $1000

2x + 3x + 5x = 1000

10x = 1000

x = 100

Therefore,

share of the first person = 2(100) = $200

share of the second person = 3(100) = $300

share of the third person = 5(100) = $500

Problem 3 :

Find the inverse ratio of 12 : 13.

Solution :

The inverse ratio of 12 : 13 is 13 : 12.

Problem 4 :

If x : 2 and 5 : 6 are inverse to each other, find the value of x.

Solution :

Because the given two ratios are inverse to each  other, the product of the two ratios is equal 1.

(x : 2) ⋅ (5 : 6) = 1

(x/2) ⋅ (5/6) = 1

5x/12 = 1

x = 12/5

Problem 5 :

Two numbers are in the ratio 2 : 3. If 4 be subtracted from each, they are in the ratio 3 : 5.  Find the numbers.

Solution :

From the given ratio 2 : 3, we have

first number = 2x

second number = 3x

From the information "If 4 be subtracted from each, they are in the ratio 3:5", we have

(2x - 4) : (3x - 4) = 3:5

Using cross product rule of proportion, we have

5(2x - 4) = 3(3x - 4)

10x - 20 = 9x - 12

x = 8

Therefore,

the first number = 2(8) = 16

the second number = 3(8) = 24

Problem 6 :

Find the compound ratio of 2 : 3, 9 : 4  and 5 : 6.

Solution :

Compound ratio of 2 : 3, 9 : 4 and 5 : 6 is

= (2 ⋅ 9 ⋅ 5)  :  (3 ⋅ 4 ⋅ 6)

= 90 : 72

= 5 : 4

Hence, the compound ratio of 2 : 3, 9 : 4 and 5 : 6 is 5 : 4.

Problem 7 :

Find the ratio of 2 hours and 115 minutes.

Solution :

2 hours = 2 ⋅ 60 = 120 minutes

2 hrs : 115 min = 120 min : 115 min

2 hrs : 115 min = 24 : 23

Hence, the ratio of 2 hours and 115 minutes is 24 : 23.

Problem 8 :

Find the ratio of $2.8 and $1.4

Solution :

$2.8 : $1.4 = (2.8 ⋅ 10) : (1.4 ⋅ 10)

$2.8 : $1.4 = 28 : 14

$2.8 : $1.4 = 2 : 1

Hence, the ratio of $2.8 and $1.4 is 2 : 1.

Problem 9 :

Find the duplicate ratio of 5 : 6.

Solution :

Duplicate ratio of 5 : 6 is

= 5² : 6²

= 25 : 36

Hence, the duplicate ratio of 5 : 6 is 25 : 36.

Problem 10 :

Find the triplicate ratio of 2 : 3.

Solution :

Triplicate ratio of 2 : 3 is

= 2³ : 3³

= 8 : 27

Hence, the triplicate ratio of 2 : 3 is 8 : 27.

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