RATIO AND PROPORTION PROBLEMS AND SOLUTIONS FOR CLASS 7

About ratio and proportion problems and solutions for class 7

On this web page "Ratio and proportion problems and solutions for class 7", we are going to have some problems and solutions in  the topic ratio and proportion which are appropriate  for the students who are in class 7.

Now let us have some problems and solutions on ratio and proportion on this web page named "Ratio and proportion problems and solutions for class 7"

Ratio and proportion problems and solutions for class 7

Question : 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,

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.

Question : 2

If $1000 is divided among the three people in the ratio 2:3:5, find the share of each. 

Solution :

Share of the first person = 2x

Share of the second person = 3x

Share of the third person = 5x

Total Amount = $1000

That is, 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

Question : 3

Find the inverse ratio of 12: 13 

Solution :

The inverse ratio of 12:13 is 13:12

Question : 4

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

Solution :

Since the given two ratios are inverse to each  other,

the product of the two ratios = 1

(x:2)X(5:6) = 1

(x/2)X(5/6) = 1

5x/12 = 1

x = 12/5

Question : 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

Question : 6

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

Solution :

Compound ratio of 2:3, 9:4 and 5:6  = (2x9x5) = (3x4x6)

= 90 : 72

= 5 : 4

Question : 7

Find the ratio of 2 hours and 115 minutes. 

Solution :

2 hours = 2x60 = 120 minutes

Ratio of 2 hrs and 115 min = 120 : 115

= 24:23

Question : 8

Find the ratio of $2.8 and $1.4 

Solution :

$2.8 : $1.4 = (2.8x10) : (1.4x10)

= 28:14

= 2 : 1

Question : 9

Find the duplicate ratio of 5:6. 

Solution :

Duplicate ratio of 5:6 = 5² : 6²

= 25 : 36

Question : 10

Find the triplicate ratio of 2:3. 

Solution :

Triplicate ratio of 2:3 = 2³  : 3³

= 8 : 27

The problems given on this page "Ratio and proportion problems and solution for class 7" would be much useful for the students who study the topic ratio and proportion in 7th grade.

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