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# Balbharati solutions for Maharashtra state board Class 9 Mathematics 1 Algebra chapter 4 - Ratio and Proportion [Latest edition]

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## Chapter 4: Ratio and Proportion

Practice Set 4.1Practice Set 4.2Practice Set 4.3Practice Set 4.4Practice Set 4.5Problem Set 4

#### Balbharati solutions for Maharashtra state board Class 9 Mathematics 1 Algebra Chapter 4 Ratio and Proportion Exercise Practice Set 4.1 [Page 61]

Practice Set 4.1 | Q 1.1 | Page 61

From the following pairs of numbers, find the reduced form of ratio of first number to second number.
72, 60

Practice Set 4.1 | Q 1.2 | Page 61

From the following pairs of numbers, find the reduced form of ratio of first number to second number.
38, 57

Practice Set 4.1 | Q 1.3 | Page 61

From the following pairs of numbers, find the reduced form of ratio of first number to second number.
52, 78

Practice Set 4.1 | Q 2.1 | Page 61

Find the reduced form of the ratio of the first quantity to second quantity.
700 rs, 308 rs

Practice Set 4.1 | Q 2.2 | Page 61

Find the reduced form of the ratio of the first quantity to second quantity.
14 rs, 12 rs. 40 paise

Practice Set 4.1 | Q 2.3 | Page 61

Find the reduced form of the ratio of the first quantity to second quantity.
5 litre, 2500 ml

Practice Set 4.1 | Q 2.3 | Page 61

Express the following percentage as ratios in the reduced form.
6.25%

Practice Set 4.1 | Q 2.4 | Page 61

Find the reduced form of the ratio of the first quantity to second quantity.
3 years 4 months, 5years 8 months

Practice Set 4.1 | Q 2.5 | Page 61

Find the reduced form of the ratio of the first quantity to second quantity.
3.8 kg, 1900 gm

Practice Set 4.1 | Q 2.6 | Page 61
Find the reduced form of the ratio of the first quantity to second quantity.
7 minutes 20 seconds,  5 minutes 6 seconds.
Practice Set 4.1 | Q 3.1 | Page 61

Express the following percentage as ratio in the reduced form.
75 : 100

Practice Set 4.1 | Q 3.2 | Page 61

Express the following percentage as ratio in the reduced form.
44 : 100

Practice Set 4.1 | Q 3.4 | Page 61

Express the following percentage as ratio in the reduced form.
52 : 100

Practice Set 4.1 | Q 3.5 | Page 61

Express the following percentage as ratio in the reduced form.
0.64%

Practice Set 4.1 | Q 4 | Page 61

Three persons can build a small house in 8 days. To build the same house in 6 days, how many persons are required?

Practice Set 4.1 | Q 5.1 | Page 61

Convert the following ratio into percentage.
15 : 25

Practice Set 4.1 | Q 5.2 | Page 61

Convert the following ratio into percentage.
47 : 50

Practice Set 4.1 | Q 5.3 | Page 61

Convert the following ratio into percentage.
7/10

Practice Set 4.1 | Q 5.4 | Page 61

Convert the following ratio into percentage.
546 / 600

Practice Set 4.1 | Q 5.5 | Page 61

Convert the following ratio into percentage.
7/16

Practice Set 4.1 | Q 6 | Page 61

The ratio of ages of Abha and her mother is 2 : 5. At the time of Abha's birth her mothers age was 27 year. Find the present ages of Abha and her mother.

Practice Set 4.1 | Q 7 | Page 61

Present ages of Vatsala and Sara are 14 years and 10 years respectively. After how many years the ratio of their ages will become 5 : 4?

Practice Set 4.1 | Q 8 | Page 61

The ratio of present ages of Rehana and her mother is 2 : 7. After 2 years, the ratio of their ages will be 1 : 3. What is Rehana's present age ?

#### Balbharati solutions for Maharashtra state board Class 9 Mathematics 1 Algebra Chapter 4 Ratio and Proportion Exercise Practice Set 4.2 [Pages 63 - 64]

Practice Set 4.2 | Q 1.1 | Page 63

Using the property a/b = (ak)/(bk) , fill in the blanks substituting proper numbers in the following.
5/7 = (.......)/28 = 35/(.......) = (.........)/3.5

Practice Set 4.2 | Q 1.2 | Page 63

Using the property a/b = (ak)/(bk) , fill in the blanks substituting proper numbers in the following.
9/14 = 4.5/(.......) = (........)/ 42 = (......) /3.5

Practice Set 4.2 | Q 2.1 | Page 63
Find the following ratio.
The ratio of radius to circumference of the circle.
Practice Set 4.2 | Q 2.2 | Page 63
Find the following ratio.
The ratio of circumference of circle with radius r to its area.
Practice Set 4.2 | Q 2.3 | Page 63
Find the following ratio.
The ratio of diagonal of a square to its side, if the length of side is 7 cm.
Practice Set 4.2 | Q 2.4 | Page 63
Find the following ratio.
The lengths of sides of a rectangle are 5 cm and 3.5 cm. Find the ratio of its perimeter to area.
Practice Set 4.2 | Q 3.1 | Page 63

Compare the following pair of ratios.
sqrt5/3 , 3/ sqrt7

Practice Set 4.2 | Q 3.2 | Page 63

Compare the following pair of ratios.
(3sqrt5)/(5sqrt7) , sqrt 63 / sqrt 125

Practice Set 4.2 | Q 3.3 | Page 63

Compare the following pair of ratios.
5/18 ,17/121

Practice Set 4.2 | Q 3.4 | Page 63

Compare the following pair of ratios.
sqrt80/sqrt48 , sqrt45/sqrt27

Practice Set 4.2 | Q 3.5 | Page 63

Compare the following pair of ratios.
9.2/5.1 , 3.4/7.1

Practice Set 4.2 | Q 4.1 | Page 63

square ABCD is a parallelogram. the ration of angleA and angleB of this parallelogram is 5 : 4. Find the measure of angleB.

Practice Set 4.2 | Q 4.2 | Page 63

The ratio of present ages of Albert and Salim is 5 : 9. Five years hence ratio of their ages will be 3 : 5. Find their present ages.

Practice Set 4.2 | Q 4.3 | Page 63

The ratio of length and breadth of a rectangle is 3 : 1, and its perimeter is 36 cm. Find the length and breadth of the rectangle.

Practice Set 4.2 | Q 4.4 | Page 63

The ratio of two numbers is 31 : 23 and their sum is 216. Find these numbers.

Practice Set 4.2 | Q 4.5 | Page 63

If the product of two numbers is 360 and their ratio is 10 : 9, then find the numbers.

Practice Set 4.2 | Q 5.1 | Page 64

If a : b = 3 : 1 and b : c = 5 : 1 then find the value of
(a^3/{15b^2c})^3

Practice Set 4.2 | Q 5.2 | Page 64

If a : b = 3 : 1 and b : c = 5 : 1 then find the value of
a^2/ (7bc)

Practice Set 4.2 | Q 6 | Page 64

If sqrt(0.04 xx 0.4 xx a ) = 0.4 xx0.04 xx sqrtb then find the ratio a/b.

Practice Set 4.2 | Q 7 | Page 64

( x + 3) : ( x + 11) = ( x - 2) : ( x + 1) then find the value of x.

#### Balbharati solutions for Maharashtra state board Class 9 Mathematics 1 Algebra Chapter 4 Ratio and Proportion Exercise Practice Set 4.3 [Page 70]

Practice Set 4.3 | Q 1.1 | Page 70

If a/b = 7/3 then find the value of the following  ratio.
(5a + 3b)/( 5a - 3b)

Practice Set 4.3 | Q 1.2 | Page 70

If a/b = 7/3 then find the value of the following  ratio.
(2a^2 + 3b^2)/(2a^2 - 3b^2)

Practice Set 4.3 | Q 1.3 | Page 70

If (a^3 - b^3)/b^3 then find the value of the following  ratio.

Practice Set 4.3 | Q 1.4 | Page 70

If a/b = 7/3 then find the value of the following  ratio.
(7a + 9b)/(7a - 9b)

Practice Set 4.3 | Q 2.1 | Page 70

If (15a^2 + 4b^2)/( 15a^2 - 4b^2) = 47/7 then find the value of following ratio.
a/b

Practice Set 4.3 | Q 2.2 | Page 70

If ( 15a^2 + 4b^2)/( 15^2 - 4b^2) = 47/7  then find the value of following ratio.

( 7a - 3b )/ ( 7a + 3b)

Practice Set 4.3 | Q 2.3 | Page 70

If If (15a^2 + 4b^2)/( 15a^2 - 4b^2) = 47/7 then find the value of following ratio.
[ b^2 - 2a^2]/[ b^2 + 2a^2]

Practice Set 4.3 | Q 2.4 | Page 70

If (15a^2 + 4b^2)/( 15a^2 - 4b^2) = 47/7 then find the value of following ratio.
[ b^3 - 2a^3]/[ b^3 + 2a^3]

Practice Set 4.3 | Q 3 | Page 70

If ( 3a + 7b)/( 3a - 7b) = 4/3 then find the value of the  ratio (3a^2 - 7b^2)/(3a^2 + 7b^2)

Practice Set 4.3 | Q 4.1 | Page 70

Solve the following equation.
(x^2 + 12x -20)/( 3x - 5 ) = (x^2 + 8x + 12)/( 2x + 3 )

Practice Set 4.3 | Q 4.2 | Page 70

Solve the following equation
[10x^2 + 15x + 63]/[5x^2 - 25x + 12] = (2x + 3)/( x -5)

Practice Set 4.3 | Q 4.3 | Page 70

Solve the following equation
[( 2x + 1)^2 + (2x - 1)^2]/[(2x + 1)^2 - (2x - 1)^2] = 17/8

Practice Set 4.3 | Q 4.4 | Page 70

Solve the following equation.
[sqrt( 4x + 1) + sqrt( x + 3 )]/[sqrt( 4x + 1 ) - sqrt( x+3 )]=4/1

Practice Set 4.3 | Q 4.5 | Page 70

Solve the following equation
 [(4x +1)^2 + ( 2x + 3)^2]/[4x^2 + 12x + 9] = 61/36

Practice Set 4.3 | Q 4.6 | Page 70

Solve the following equation
[(3x - 4)^3 - ( x + 1)^3]/[( 3x - 4)^3 + ( x + 1)^3] = 61/189

#### Balbharati solutions for Maharashtra state board Class 9 Mathematics 1 Algebra Chapter 4 Ratio and Proportion Exercise Practice Set 4.4 [Pages 73 - 74]

Practice Set 4.4 | Q 1.1 | Page 73

Fill in the blanks of the following
x/7 = y/3 = (3x + 5y)/(..........) = (7x -9y)/(.........)

Practice Set 4.4 | Q 1.2 | Page 73

Fill in the blanks of the following
a/3 = b/4 = c/7 = (a-2b+3c)/(............) = (..............)/ ( 6 - 8 +14 )

Practice Set 4.4 | Q 2.1 | Page 73

5m - n = 3m + 4n  then find the value of the following expression.
[m^2 + n^2]/[m^2 + n^2]

Practice Set 4.4 | Q 2.2 | Page 73

5m - n = 3m + 4n  then find the value of the following expression.
(3m + 4n)/(3m - 4n)

Practice Set 4.4 | Q 3.1 | Page 73

If a(y+z) = b(z+x) = c(x+y) and out of a, b, c no two of them are equal  then  show that,
(y - z)/[a ( b - c )] = ( z - x)/[ b ( c - a)] = ( x - y)/[c ( a - b )]

Practice Set 4.4 | Q 3.3 | Page 73

If  [ax + by]/( x + y) = ( bx + az )/( x + z ) = ( ay + bz )/[ y + z ]and x + y + z ≠ 0  then show that [a + b]/2.

Practice Set 4.4 | Q 3.4 | Page 73

If    ( y + z)/a = ( z + x )/b = ( x + y )/ c  then show that x/[ b + c - a ] = y/[ c + a - b ] = z / ( a + b - c)

Practice Set 4.4 | Q 4.1 | Page 74

Solve
[ 16x^2 - 20x +9]/[ 8x^2 + 12x + 21] = ( 4x - 5 )/( 2x + 3)

Practice Set 4.4 | Q 4.2 | Page 73

If x/[3x - y -z] = y/[3y - z -x] = z/[3z -x -y] and x + y + z ≠ 0 then show that the value of each ratio is equal to 1.

Practice Set 4.4 | Q 4.2 | Page 74

Solve
( 5y^2 + 40y - 12)/( 5y + 10y^2 - 4) = ( y + 8)/( 1 + 2y)

Practice Set 4.4 | Q 4.5 | Page 73

If { 3x - 5y }/ ( 5z + 3y ) = ( x + 5z )/( y - 5x ) = ( y - z )/ ( x - z )then show that every ratio = x/y.

#### Balbharati solutions for Maharashtra state board Class 9 Mathematics 1 Algebra Chapter 4 Ratio and Proportion Exercise Practice Set 4.5 [Page 77]

Practice Set 4.5 | Q 1 | Page 77

Which number should be subtracted from 12, 16 and 21 so that resultant numbers are in continued proportion?

Practice Set 4.5 | Q 2 | Page 77

If ( 28 - x)  is the mean proportional of ( 23 - x)and ( 19 - x) then find the vaue of x.

Practice Set 4.5 | Q 3 | Page 77

Three numbers are in continued proportion, whose mean proportional is 12 and the sum of the remaining two numbers is 26, then find these numbers.

Practice Set 4.5 | Q 4 | Page 77

If (a + b + c) (a - b + c) = a+ b+ cshow that a, b, c are in continued proportion.

Practice Set 4.5 | Q 5.1 | Page 77

If a/b = b/c and  a , b , c > 0 then show that,
(a + b + c) (b - c) = ab - c

Practice Set 4.5 | Q 5.2 | Page 77
If a/b = b/c  and a,b,c > 0 then show that,
(a+ b2) (b+ c) = (ab + bc)
Practice Set 4.5 | Q 5.3 | Page 77

If a/b = b/c  and a,b,c > 0 then show that,
[a^2 + b^2]/ab = (a+c)/b

Practice Set 4.5 | Q 6 | Page 77

Find mean proportional of ( x + y)/( x - y), (x^2 - y^2)/(x^2y^2)

#### Balbharati solutions for Maharashtra state board Class 9 Mathematics 1 Algebra Chapter 4 Ratio and Proportion Exercise Problem Set 4 [Pages 77 - 79]

Problem Set 4 | Q 1.1 | Page 77

Select the appropriate alternative answer for the following question.
If 6 : 5 = y : 20 then what will be the value of y ?

• 15

• 24

• 18

• 22.5

Problem Set 4 | Q 1.2 | Page 77

Select the appropriate alternative answer for the following question.
What is the ratio of 1 mm to 1 cm ?

• 1 : 100

• 10 : 1

• 1 : 10

• 100 : 1

Problem Set 4 | Q 1.3 | Page 77

Select the Appropriate Alternative Answer for the Following Question.
The ages of Jatin, Nitin and Mohasin are 16, 24 and 36 years respectively. What is the ratio of Nitin’s age to Mohasin’s age ?

• 3 : 2

• 2 : 3

• 4 : 3

• 3 : 4

Problem Set 4 | Q 1.4 | Page 77

Select the Appropriate Alternative Answer for the Following Question.

24 Bananas were distributed between Shubham and Anil in the ratio 3 : 5, then how many bananas did Shubham get ?

• 8

• 15

• 12

• 9

Problem Set 4 | Q 1.5 | Page 77

Select the Appropriate Alternative Answer for the Following Question.

What is the mean proportional of 4 and 25 ?

• 6

• 8

• 10

• 12

Problem Set 4 | Q 2.1 | Page 78

For the following numbers write the ratio of first number to second number in the reduced form.
21 , 48

Problem Set 4 | Q 2.2 | Page 78

For the following numbers write the ratio of first number to second number in the reduced form.
36, 90

Problem Set 4 | Q 2.3 | Page 78

For the following numbers write the ratio of first number to second number in the reduced form.
65, 117

Problem Set 4 | Q 2.4 | Page 78

For the following numbers write the ratio of first number to second number in the reduced form.
138 , 161

Problem Set 4 | Q 2.5 | Page 78

For the following numbers write the ratio of first number to second number in the reduced form.
114, 133

Problem Set 4 | Q 3.1 | Page 78

Write the following ratio in the reduced form.
Radius to the diameter of a circle.

Problem Set 4 | Q 3.2 | Page 78

Write the Following Ratio in the Reduced Form.
The ratio of diagonal to the length of a rectangle, having length 4 cm and breadth 3 cm.

Problem Set 4 | Q 3.3 | Page 78

Write the following ratio in the reduced form.
The ratio of perimeter to area of a square, having side 4 cm.

Problem Set 4 | Q 4.1 | Page 78

Check whether the following numbers are in continued proportion.
2, 4, 8

Problem Set 4 | Q 4.2 | Page 78

Check whether the following numbers are in continued proportion.
1, 2, 3

Problem Set 4 | Q 4.3 | Page 78

Check whether the following numbers are in continued proportion.
9, 12, 16

Problem Set 4 | Q 4.4 | Page 78

Check whether the following numbers are in continued proportion.
3, 5, 8

Problem Set 4 | Q 5 | Page 78

a, b, c are in continued proportion. If a = 3 and c = 27 then find b.

Problem Set 4 | Q 6.1 | Page 78

Convert the following ratio into percentage.
37 : 500

Problem Set 4 | Q 6.2 | Page 78

Convert the following ratio into percentage.
5/8

Problem Set 4 | Q 6.3 | Page 78

Convert the following ratio into percentage
22/30

Problem Set 4 | Q 6.4 | Page 78

Convert the following ratio into percentage.
5/16

Problem Set 4 | Q 6.5 | Page 78

Convert the following ratio into percentage
144/1200

Problem Set 4 | Q 7.1 | Page 78

Write the ratio of first quantity to second quantity in the reduced form.
1024 MB, 1.2 GB (1024 MB = 1 GB)

Problem Set 4 | Q 7.2 | Page 78

Write the ratio of first quantity to second quantity in the reduced form.
17 Rupees, 25 Rupees 60 paise

Problem Set 4 | Q 7.3 | Page 78

Write the ratio of first quantity to second quantity in the reduced form.
5 dozen, 120 units

Problem Set 4 | Q 7.4 | Page 78

Write the ratio of first quantity to second quantity in the reduced form.
4 sq.m, 800 sq.cm

Problem Set 4 | Q 7.5 | Page 78

Write the ratio of first quantity to second quantity in the reduced form.
1.5 kg, 2500 gm

Problem Set 4 | Q 8.1 | Page 78

If a/b = 2/3  then find the value of the following expression.

[ 4a + 3b ]/( 3b )

Problem Set 4 | Q 8.2 | Page 78

If a/b = 2/3  then find the value of the following expression.

[ 5a^2 + 2b^2]/[ 5a^2 - 2b^2]

Problem Set 4 | Q 8.3 | Page 78

If a/b = 2/3  then find the values of the following expression

[a^3 + b^3]/b^3

Problem Set 4 | Q 8.4 | Page 78

If a/b = 2/3  then find the value of the following expression.

[ 7b - 4b]/[ 7b + 4a ]

Problem Set 4 | Q 9.1 | Page 78

If a, b, c, d   are in proportion , then prove that
[ 11a^2 + 9ac]/[ 11b^2 + 9bd] = [ a^2 + 3ac]/[ b^2 + 3bd]

Problem Set 4 | Q 9.2 | Page 78

If a, b, c, d   are in proportion , then prove that
sqrt[( a^2 + 5c^2)/( b^2 + 5d^2)] = a/d

Problem Set 4 | Q 9.3 | Page 78

If a, b, c, d   are in proportion , then prove that

[a^2 + ab + b^2]/[a^2 - ab + b^2] = [c^2 + cd + d^2 ]/[ c^2 - cd + d^2 ]

Problem Set 4 | Q 10.1 | Page 79

If   a, b, c  are in continued proportion , then prove that
a/[ a + 2b] = [a - 2b]/[ a - 4c]

Problem Set 4 | Q 10.2 | Page 79

If   a, b, c  are in continued proportion , then prove that

b/[b+c] = [a-b]/[a-c]

Problem Set 4 | Q 11 | Page 79

Solve:
[12x^2 + 18x + 42]/[ 18 x^2 + 12x +58 ] = [ 2x + 3]/[ 3x + 2]

Problem Set 4 | Q 12 | Page 79

If [ 2x - 3y ]/[ 3z + y] = [ z - y ]/[ z - x ] = [ x + 3z ]/[ 2y - 3z ] then prove that every ratio = x/y.

Problem Set 4 | Q 13 | Page 79

If [ by + cz ]/[ b^2 + c^2] = [ cz + ax ]/[ c^2 + a^2] = [ ax + by ]/[ a^2 + b^2 ]

then prove that x/a= y/b = z/c

## Chapter 4: Ratio and Proportion

Practice Set 4.1Practice Set 4.2Practice Set 4.3Practice Set 4.4Practice Set 4.5Problem Set 4

## Balbharati solutions for Maharashtra state board Class 9 Mathematics 1 Algebra chapter 4 - Ratio and Proportion

Balbharati solutions for Maharashtra state board Class 9 Mathematics 1 Algebra chapter 4 (Ratio and Proportion) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Maharashtra State Board Maharashtra state board Class 9 Mathematics 1 Algebra solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Maharashtra state board Class 9 Mathematics 1 Algebra chapter 4 Ratio and Proportion are Introduction of Ratio and Proportion, Properties of Ratio, Comparison of Ratios, Operations on Equal Ratios, Application of Properties of Equal Ratios, Theorem on Equal Ratios, Continued Proportion.

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