Balbharati solutions for Algebra (Mathematics 1) [English] 9 Standard Maharashtra State Board chapter 4 - Ratio and Proportion [Latest edition]

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

72, 60

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

38, 57

From the following pair 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, ₹ 308

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

₹ 14, ₹ 12. 40 paise

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

5 litre, 2500 ml

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

3 years 4 months, 5 years 8 months

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

3.8 kg, 1900 gm

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

7 minutes 20 seconds,  5 minutes 6 seconds

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 ratios in the reduced form.

6.25%

Express the following percentage as a 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?

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

`5/7 = ("___")/28 = 35/("___") = ("___")/3.5`

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

`9/14 = 4.5/("___") = ("___")/ 42 = ("___") /3.5`

Find the following ratio.

The ratio of radius to circumference of the circle.

Find the following ratio.

The ratio of circumference of circle with radius r to its area.

Find the following ratio.

The ratio of diagonal of a square to its side, if the length of side is 7 cm.

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.

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 ratio 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.

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

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

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

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

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

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

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

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

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

`a/b`

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

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

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

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

If `bb((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`

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 `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.

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)`

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

Solve. 

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

Solve. 

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

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 value 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) = a² + b² + c² 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 - c² 

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)`

If 6 : 5 = y : 20 then what will be the value of y?

What is the ratio of 1 mm to 1 cm?

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?

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

What is the mean proportional of 4 and 25?

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 the 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 `bb(a/b = 2/3)` then find the value of the following expression.

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

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

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

If `bb("a"/"b" = 2/3)`  then find the values of the following expression

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

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

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

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 - 3x]` 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`