#### Chapters

## Chapter 4: Ratio and Proportion

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

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

72, 60

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

38, 57

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

52, 78

Find the reduced form of the ratio of the first quantity to second quantity.

700 rs, 308 rs

Find the reduced form of the ratio of the first quantity to second quantity.

14 rs, 12 rs. 40 paise

Find the reduced form of the ratio of the first quantity to second quantity.

5 litre, 2500 ml

Express the following percentage as ratios in the reduced form.

6.25%

Find the reduced form of the ratio of the first quantity to second quantity.

3 years 4 months, 5years 8 months

Find the reduced form of the ratio of the first quantity to second quantity.

3.8 kg, 1900 gm

Express the following percentage as ratio in the reduced form.

75 : 100

Express the following percentage as ratio in the reduced form.

44 : 100

Express the following percentage as ratio in the reduced form.

52 : 100

Express the following percentage as ratio in the reduced form.

0.64%

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

Convert the following ratio into percentage.

15 : 25

Convert the following ratio into percentage.

47 : 50

Convert the following ratio into percentage.

`7/10`

Convert the following ratio into percentage.

`546 / 600`

Convert the following ratio into percentage.

`7/16`

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.

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?

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]

Using the property `a/b = (ak)/(bk)` , fill in the blanks substituting proper numbers in the following.

`5/7` = `(.......)/28 = 35/(.......) = (.........)/3.5`

Using the property `a/b = (ak)/(bk)` , fill in the blanks substituting proper numbers in the following.

`9/14 = 4.5/(.......) = (........)/ 42 = (......) /3.5`

Compare the following pair of ratios.

`sqrt5/3 , 3/ sqrt7`

Compare the following pair of ratios.

`(3sqrt5)/(5sqrt7) , sqrt 63 / sqrt 125`

Compare the following pair of ratios.

`5/18 ,17/121`

Compare the following pair of ratios.

`sqrt80/sqrt48 , sqrt45/sqrt27`

Compare the following pair of ratios.

`9.2/5.1 , 3.4/7.1`

`square` ABCD is a parallelogram. the ration of `angle`A and `angle`B of this parallelogram is 5 : 4. Find the measure of `angle`B.

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.

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.

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

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

If a : b = 3 : 1 and b : c = 5 : 1 then find the value of

`(a^3/{15b^2c})^3`

If a : b = 3 : 1 and b : c = 5 : 1 then find the value of

`a^2/ (7bc)`

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

( 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]

If `a/b = 7/3` then find the value of the following ratio.

`(5a + 3b)/( 5a - 3b)`

If `a/b = 7/3` then find the value of the following ratio.

`(2a^2 + 3b^2)/(2a^2 - 3b^2)`

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

If `a/b = 7/3` then find the value of the following ratio.

`(7a + 9b)/(7a - 9b)`

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

`a/b`

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

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

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]`

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]`

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

Solve the following equation.

`(x^2 + 12x -20)/( 3x - 5 ) = (x^2 + 8x + 12)/( 2x + 3 )`

Solve the following equation

`[10x^2 + 15x + 63]/[5x^2 - 25x + 12] = (2x + 3)/( x -5)`

Solve the following equation

`[( 2x + 1)^2 + (2x - 1)^2]/[(2x + 1)^2 - (2x - 1)^2] = 17/8`

Solve the following equation.

`[sqrt( 4x + 1) + sqrt( x + 3 )]/[sqrt( 4x + 1 ) - sqrt( x+3 )]=4/1`

Solve the following equation

` [(4x +1)^2 + ( 2x + 3)^2]/[4x^2 + 12x + 9] = 61/36`

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]

Fill in the blanks of the following

`x/7 = y/3 = (3x + 5y)/(..........) = (7x -9y)/(.........)`

Fill in the blanks of the following

`a/3 = b/4 = c/7 = (a-2b+3c)/(............) = (..............)/ ( 6 - 8 +14 )`

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

`[m^2 + n^2]/[m^2 + n^2]`

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

`(3m + 4n)/(3m - 4n)`

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 )]`

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

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)`

Solve

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

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.

Solve

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

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]

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

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

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.

If (a + b + c) (a - b + c) = a^{2 }+ b^{2 }+ c^{2 }show that a, b, c are in continued proportion.

If `a/b = b/c` and `a , b , c > 0` then show that,

(a + b + c) (b - c) = ab - c^{2 }

^{2 }+ b

^{2}) (b

^{2 }+ c

^{2 }) = (ab + bc)

^{2 }

If `a/b = b/c` and `a,b,c > 0` then show that,

`[a^2 + b^2]/ab = (a+c)/b`

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]

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

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

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

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

Select the Appropriate Alternative Answer for the Following Question.

What is the mean proportional of 4 and 25 ?

6

8

10

12

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

21 , 48

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

36, 90

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

65, 117

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

138 , 161

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

114, 133

Write the following ratio in the reduced form.

Radius to the diameter of a circle.

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.

Write the following ratio in the reduced form.

The ratio of perimeter to area of a square, having side 4 cm.

Check whether the following numbers are in continued proportion.

2, 4, 8

Check whether the following numbers are in continued proportion.

1, 2, 3

Check whether the following numbers are in continued proportion.

9, 12, 16

Check whether the following numbers are in continued proportion.

3, 5, 8

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

Convert the following ratio into percentage.

37 : 500

Convert the following ratio into percentage.

`5/8`

Convert the following ratio into percentage

`22/30`

Convert the following ratio into percentage.

`5/16`

Convert the following ratio into percentage

`144/1200`

Write the ratio of first quantity to second quantity in the reduced form.

1024 MB, 1.2 GB (1024 MB = 1 GB)

Write the ratio of first quantity to second quantity in the reduced form.

17 Rupees, 25 Rupees 60 paise

Write the ratio of first quantity to second quantity in the reduced form.

5 dozen, 120 units

Write the ratio of first quantity to second quantity in the reduced form.

4 sq.m, 800 sq.cm

Write the ratio of first quantity to second quantity in the reduced form.

1.5 kg, 2500 gm

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

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

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

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

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

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

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

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

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

`[ 11a^2 + 9ac]/[ 11b^2 + 9bd] = [ a^2 + 3ac]/[ b^2 + 3bd]`

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

`sqrt[( a^2 + 5c^2)/( b^2 + 5d^2)] = a/d`

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 ]`

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

`a/[ a + 2b] = [a - 2b]/[ a - 4c]`

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

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

Solve:

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

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

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

## 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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