# RATIO AND PROPORTION WORKSHEETS WITH ANSWERS

Ratio and Proportion Worksheets with Answers :

Worksheet given in this section will be much useful for the students who would like to practice problems on ratio and proportion.

## Ratio and Proportion Worksheet - Questions

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.

Question : 2

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

Question : 3

Find the inverse ratio of 12 : 13.

Question : 4

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

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.

Question : 6

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

Question : 7

Find the ratio of 2 hours and 115 minutes.

Question : 8

Find the ratio of \$2.8 and \$1.4

Question : 9

Find the duplicate ratio of 5 : 6.

Question : 10

Find the triplicate ratio of 2 : 3.

## Ratio and Proportion Worksheet - Solutions

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, 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

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 :

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

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 is

=  (2 ⋅ ⋅ 5)  :  (3 ⋅ ⋅ 6)

=  90 : 72

=  5 : 4

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

Question : 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.

Question : 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.

Question : 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.

Question : 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.

After having gone through the stuff given above, we hope that the students would have understood, how to solve problems on ratio and proportion.

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

You can also visit our following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6