Maharashtra Board Class 9 Maths Solutions Chapter 4 Ratio and Proportion Practice Set 4.3

Maharashtra Board Class 9 Maths Solutions Chapter 4 Ratio and Proportion Practice Set 4.3

Question 1.
If \(\frac { a }{ b }\) = \(\frac { 7 }{ 3 }\), then find the aIues of the following ratios.
Maharashtra Board Class 9 Maths Solutions Chapter 4 Ratio and Proportion Practice Set 4.3 1
Solution:
Maharashtra Board Class 9 Maths Solutions Chapter 4 Ratio and Proportion Practice Set 4.3 2
Maharashtra Board Class 9 Maths Solutions Chapter 4 Ratio and Proportion Practice Set 4.3 3
Maharashtra Board Class 9 Maths Solutions Chapter 4 Ratio and Proportion Practice Set 4.3 4
Maharashtra Board Class 9 Maths Solutions Chapter 4 Ratio and Proportion Practice Set 4.3 5
Maharashtra Board Class 9 Maths Solutions Chapter 4 Ratio and Proportion Practice Set 4.3 6

Question 2.
If \(\frac{15 a^{2}+4 b^{2}}{15 a^{2}-4 b^{2}}=\frac{47}{7}\), then find the value of the following ratios.
Maharashtra Board Class 9 Maths Solutions Chapter 4 Ratio and Proportion Practice Set 4.3 7
Solution:
Maharashtra Board Class 9 Maths Solutions Chapter 4 Ratio and Proportion Practice Set 4.3 8
Maharashtra Board Class 9 Maths Solutions Chapter 4 Ratio and Proportion Practice Set 4.3 9
Maharashtra Board Class 9 Maths Solutions Chapter 4 Ratio and Proportion Practice Set 4.3 10
Maharashtra Board Class 9 Maths Solutions Chapter 4 Ratio and Proportion Practice Set 4.3 11

Question 3.
If \(\frac{3 a+7 b}{3 a-7 b}=\frac{4}{3}\)then find the value of the ratio \(\frac{3 a^{2}-7 b^{2}}{3 a^{2}+7 b^{2}}\).
Solution:
Maharashtra Board Class 9 Maths Solutions Chapter 4 Ratio and Proportion Practice Set 4.3 12
Maharashtra Board Class 9 Maths Solutions Chapter 4 Ratio and Proportion Practice Set 4.3 13

Question 4.
Solve the following equations.
Maharashtra Board Class 9 Maths Solutions Chapter 4 Ratio and Proportion Practice Set 4.3 14
Solution:
Maharashtra Board Class 9 Maths Solutions Chapter 4 Ratio and Proportion Practice Set 4.3 15
This equation is true for x = 0
∴ x = 0 is one of the solutions.
If x ≠ 0, then x2 ≠ 0
∴ \(\frac { 1 }{ 12x – 20 }\) = \(\frac { 1 }{ 8x + 12 }\) … [Dividing both sides by x2]
∴ 8x + 12 = 12x – 20
∴ 12 + 20 = 12x – 8x
∴ 32 = 4x
∴ x = 8
∴ x = 0 or x = 8 are the solutions of the given equation.

Maharashtra Board Class 9 Maths Solutions Chapter 4 Ratio and Proportion Practice Set 4.3 16
Maharashtra Board Class 9 Maths Solutions Chapter 4 Ratio and Proportion Practice Set 4.3 17
∴ 21(x – 5) = 4(2x + 3)
∴ 21x – 105 = 8x + 12
∴ 21x – 8x = 12 + 105
∴ 13x = 117
∴ x = 9
∴ x = 9 ¡s the solution of the given equation.

Maharashtra Board Class 9 Maths Solutions Chapter 4 Ratio and Proportion Practice Set 4.3 18

Maharashtra Board Class 9 Maths Solutions Chapter 4 Ratio and Proportion Practice Set 4.3 19
∴ 9(4x + 1) = 25(x + 3)
∴36x + 925x + 75
∴ 36x – 25 = 75 – 9
∴11x = 66
∴ x = 6
∴ x = 6 is the solution of the given equation.
Maharashtra Board Class 9 Maths Solutions Chapter 4 Ratio and Proportion Practice Set 4.3 20
Maharashtra Board Class 9 Maths Solutions Chapter 4 Ratio and Proportion Practice Set 4.3 21
∴ 4(3x – 4) = 5(x + 1)
∴ 12x – 16 = 5x + 5
∴ 12x – 5x = 5 + 16
∴ 7x = 21
∴ x = 3
∴ x = 3 ¡s the solution of the given equation.

Maharashtra Board Class 9 Maths Solutions

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