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Find the Ratio and Proportion (Word Problems)

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1

Divide 80 hours in the ratio 2:6

2

In a city of 384090 people, the ratio of men to women is 3 : 7. Find the number of men and women?

3

The ratio between length and breadth of a rectangle is 5:6. If the breadth is 534 inch, find the length?

4

If $3283 is divided between Kevin and Jonathan in 3:4 ratio, who will get more and how much more?

5

The ratio of expenditure and savings in a family is 4:9. If the expenditure is $2296. What is the savings?

6

Divide $994 in the ratio 5:9

7

Iva and Sophia decides to share the price money of competition in 2:3 ratio respectively. If they receive $4575 together. Find the share of each

8

The ratio between length and breadth of a rectangle is 4:2. If the breadth is 40 inch, find the length?

9

The ratio of expenditure and savings in a family is 6:8. If the expenditure is $2904. What is the savings?

10

In a city of 474621 people, the ratio of men to women is 3 : 4. Find the number of men and women?

Solved Worksheet Problems

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1

Divide 80 hours in the ratio 2:6

20 : 60

Solution

2:6 means the first quantity is 2 parts and the second quantity in 6 parts.

The total number of parts = 2 + 6 = 8

8parts = 80

∴ 2 parts = 10 x 2 = 20

and 6 parts = 10 x 6 = 60

The total number of parts = 2 + 6 = 8

8parts = 80

∴ 1 part =

808

= 10

and 6 parts = 10 x 6 = 60

2

In a city of 384090 people, the ratio of men to women is 3 : 7. Find the number of men and women?

Number of men in the city = 115227

Number of women in the city = 268863

Number of women in the city = 268863

Solution

Number of people in the city = 384090

Ratio of men to women = 3 : 7

The total number of parts = 3 + 7 = 10

10parts = 384090

∴ Number of men in the city = 38409 x 3 = 115227

and Number of women in the city = 38409 x 7 = 268863

Ratio of men to women = 3 : 7

The total number of parts = 3 + 7 = 10

10parts = 384090

∴ 1 part =

38409010

= 38409

and Number of women in the city = 38409 x 7 = 268863

3

The ratio between length and breadth of a rectangle is 5:6. If the breadth is 534 inch, find the length?

Length = 445 inch

Solution

Breadth of the rectangle = 534 inch

The ratio of length to breadth is 5:6

Breadth = 6 part

6 parts = 534 inch

Length = 5 parts

5 parts = 5 x 89 = 445

∴ Length of the rectangle = 445 inch.

The ratio of length to breadth is 5:6

Breadth = 6 part

6 parts = 534 inch

∴ 1 part =

5346

= 89

5 parts = 5 x 89 = 445

∴ Length of the rectangle = 445 inch.

4

If $3283 is divided between Kevin and Jonathan in 3:4 ratio, who will get more and how much more?

Kevin get $1407

Jonathan get $1876

Jonathan get $469 more than Kevin

Jonathan get $1876

Jonathan get $469 more than Kevin

Solution

Total Money = $3283

Ratio of Kevin and Jonathan = 3 : 4

The total number of parts = 3 + 4 = 7

7 parts = 3283

Kevin's amount = 469 x 3 = $1407

Jonathan's amount = 469 x 4 = $1876

Jonathan get 1876

Ratio of Kevin and Jonathan = 3 : 4

The total number of parts = 3 + 4 = 7

7 parts = 3283

∴ 1 part =

32837

= 469

Jonathan's amount = 469 x 4 = $1876

Jonathan get 1876

5

The ratio of expenditure and savings in a family is 4:9. If the expenditure is $2296. What is the savings?

Savings = $5166

Solution

The ratio of expenditure and savings is 4:9

Expenditure of the family = $2296

Expenditure = 4 part

4 parts = $2296

Savings = 9 parts

9 parts = 9 x 574 = 5166

∴ Savings of the family = $5166

Expenditure of the family = $2296

Expenditure = 4 part

4 parts = $2296

∴ 1 part =

22964

= 574

9 parts = 9 x 574 = 5166

∴ Savings of the family = $5166

6

Divide $994 in the ratio 5:9

$355 : $639

Solution

5:9 means the first quantity is 5 parts and the second quantity in 9 parts.

The total number of parts = 5 + 9 = 14

14 parts = $994

∴ 5 parts = 71 x 5 = $355

and 9 parts = 71 x 9 = $639

The total number of parts = 5 + 9 = 14

14 parts = $994

∴ 1 part =

99414

= 71

and 9 parts = 71 x 9 = $639

7

Iva and Sophia decides to share the price money of competition in 2:3 ratio respectively. If they receive $4575 together. Find the share of each

Iva get $1830

Sophia get $2745

Sophia get $2745

Solution

Total price money = $4575

Ratio of Iva and Sophia = 2 : 3

The total number of parts = 2 + 3 = 5

5 parts = 4575

∴ Iva's price money = 915 x 2 = $1830

and Sophia's price money = 915 x 3 = $2745

Ratio of Iva and Sophia = 2 : 3

The total number of parts = 2 + 3 = 5

5 parts = 4575

∴ 1 part =

45755

= 915

and Sophia's price money = 915 x 3 = $2745

8

The ratio between length and breadth of a rectangle is 4:2. If the breadth is 40 inch, find the length?

Length = 80 inch

Solution

Breadth of the rectangle = 40 inch

The ratio of length to breadth is 4:2

Breadth = 2 part

2 parts = 40 inch

Length = 4 parts

4 parts = 4 x 20 = 80

∴ Length of the rectangle = 80 inch.

The ratio of length to breadth is 4:2

Breadth = 2 part

2 parts = 40 inch

∴ 1 part =

402

= 20

4 parts = 4 x 20 = 80

∴ Length of the rectangle = 80 inch.

9

The ratio of expenditure and savings in a family is 6:8. If the expenditure is $2904. What is the savings?

Savings = $3872

Solution

The ratio of expenditure and savings is 6:8

Expenditure of the family = $2904

Expenditure = 6 part

6 parts = $2904

Savings = 8 parts

8 parts = 8 x 484 = 3872

∴ Savings of the family = $3872

Expenditure of the family = $2904

Expenditure = 6 part

6 parts = $2904

∴ 1 part =

29046

= 484

8 parts = 8 x 484 = 3872

∴ Savings of the family = $3872

10

In a city of 474621 people, the ratio of men to women is 3 : 4. Find the number of men and women?

Number of men in the city = 203409

Number of women in the city = 271212

Number of women in the city = 271212

Solution

Number of people in the city = 474621

Ratio of men to women = 3 : 4

The total number of parts = 3 + 4 = 7

7parts = 474621

∴ Number of men in the city = 67803 x 3 = 203409

and Number of women in the city = 67803 x 4 = 271212

Ratio of men to women = 3 : 4

The total number of parts = 3 + 4 = 7

7parts = 474621

∴ 1 part =

4746217

= 67803

and Number of women in the city = 67803 x 4 = 271212

Online Test

Start my Challenge

Divide 132 hours in the ratio 2:9

In a city of 307928 people, the ratio of men to women is 6 : 2. Find the number of men and women?

In a city of 370524 people, the ratio of men to women is 6 : 5. Find the number of men and women?

In a city of 509679 people, the ratio of men to women is 4 : 5. Find the number of men and women?

Divide 55 hours in the ratio 6:5

If $3038 is divided between Evelyn and Beatrice in 5:2 ratio, who will get more and how much more?

Question:

Write the ratio 2:6:8 in its reduced form.

Answer:

Write the ratio 2:6:8 in its reduced form.

Answer:

Find GCF of all values in the given ratio

GCF(2, 6, 8) = 2

Divide each number in the given ratio by GCF

2/2 = 1

6/2 = 3

8/2 = 4

2:6:8 = 1 : 3 : 4

The simplified ratio of 2:6:8 is 1 : 3 : 4

GCF(2, 6, 8) = 2

Divide each number in the given ratio by GCF

2/2 = 1

6/2 = 3

8/2 = 4

2:6:8 = 1 : 3 : 4

The simplified ratio of 2:6:8 is 1 : 3 : 4