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Class 9 (SSC)Mathematics & Statistics2026-27 Syllabus

Chapter 4 Ratio and Proportion Problem Set 4 Solutions

Complete Maharashtra State Board Balbharati & Yuvakbharati textbook solutions for Chapter 4 Ratio and Proportion Problem Set 4. Step-by-step solved exercises, numerical problems, and digest answers.

14 Solved Questions• 1398 words

Problem Set 4 Algebra 9th Std Maths Part 1 Answers Chapter 4 Ratio and Proportion

Question 1 Maharashtra Board Solution
Select the appropriate alternative answer for the following questions.

i. If 6 : 5 = y : 20, then what will be the value of y?
(A) 15
(B) 24
(C) 18
(D) 22.5

Solution & Step-by-Step Answer:

(B) 24

ii. What is the ratio of 1 mm to 1 cm ?
(A) 1 : 100
(B) 10: 1
(C) 1 : 10
(D) 100: 1
Answer:
(C) 1 : 10

iii. 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 ?
(A) 3 : 2
(B) 2 : 3
(C) 4 : 3
(D) 3 : 4
Answer:
(B) 2 : 3

iv. 24 bananas were distributed between Shubham and Anil in the ratio 3 : 5, then how many bananas did Shubham get?
(A) 8
(B) 15
(C) 12
(D) 9
Answer:
(D) 9

v. What is the mean proportional of 4 and 25?
(A) 6
(B) 8
(C) 10
(D) 12
Answer:
(C) 10

Hints:
i.
∴

ii.

iii.
= 2 : 3

iv. 3x + 5x = 24
∴ 8x = 24
∴ x = 3
∴ Number of bananas with Shubham = 3x = 9

v. x2= 4 x 25
∴ x2= 100
∴ x = 10

Question 2 Maharashtra Board Solution
For the following numbers write the ratio of first number to second number in the reduced form. [1 Mark each] i. 21,48 ii. 36,90 iii. 65,117 iv. 138,161 v. 114,133
Solution & Step-by-Step Answer:
i. 21,48 ii. 36,90 iii. 65,117 iv. 138,161 v. 114,133
Question 3 Maharashtra Board Solution
Write the following ratios in the reduced form. i. Radius to the diameter of a circle. ii. The ratio of diagonal to the length of a rectangle, having length 4 cm and breadth 3 cm. iii. The ratio of numbers denoting perimeter to area of a square, having side 4 cm.
Solution & Step-by-Step Answer:
i. Radius to the diameter of a circle. Let radius of the circle be r then, diameter = 2 x radius = 2r Ratio of radius to diameter of circle ∴ Ratio of radius to diameter of circle is 1 : 2.

ii. The ratio of diagonal to the length of a rectangle, having length 4 cm and breadth 3 cm.

Let □ ABCD be a rectangle.
In ∆ABC, ∠B = 90°
AC2= AB2+ BC2… [Pythagoras theorem]
= 42+ 32= 16 + 9
∴ AC2= 25
AC = 5 … [Taking square root on both side]
The ratio of diagonal to the length of a rectangle =
=
= 5 : 4
∴ The ratio of diagonal to the length of a rectangle is 5 : 4

iii. The ratio of numbers denoting perimeter to area of a square, having side 4 cm. side of square = 4cm
Perimeter of square = 4 x side = 4 x 4 = 16 cm
Area of square = (side)2= (4)2= 16 cm2
Ratio of numbers denoting perimeter to area of square

∴ The ratio of numbers denoting perimeter to area of a square is 1 : 1.

Question 4 Maharashtra Board Solution
Check whether the following numbers are in continued proportion. i. 2, 4, 8 ii. 1, 2, 3 iii. 9, 12, 16 iv. 3, 5, 8
Solution & Step-by-Step Answer:
If a, b, c are in continued proportion then b2 = ac. i. 2, 4, 8 Let, a = 2, b = 4 and c = 8 Here, b2 = 42 = 16 ac = 2 x 8 = 16 ∴ b2 = ac ∴ 2, 4,8 are in continued proportion.

ii. 1, 2, 3
Let, a = 1, b = 2 and c = 3
Here, b2= 22= 4
ac = 1 x 3 = 3
∴ b2≠ ac
∴ 1, 2,3 are not in continued proportion.

iii. 9, 12, 16
Let, a = 9, b = 12 and c = 16
Here, b2= 122= 144
ac = 9 x 16 = 144
∴ b2= ac
∴ 9, 12, 16 are in continued proportion.

iv. 3, 5, 8
Let, a = 3, b = 5 and c = 8
Here, b2= 52= 25
ac = 3 x 8 = 24
∴ b2≠ ac
∴ 3, 5, 8 are not in continued proportion.

Question 5 Maharashtra Board Solution
a, b, c are in continued proportion. If a = 3 and c = 27, then find b.
Solution & Step-by-Step Answer:
a, b, c are in continued proportion. …[Given] ∴ b2 = ac ∴ b2 = 3 x 27 …[∵ a = 3 and c = 27] ∴ b2 = 81 ∴ b = 9 …[Taking square root of both sides]
Question 6 Maharashtra Board Solution
Convert the following ratios into percentages.
Solution & Step-by-Step Answer:
i. Let 37 : 500 = x% ∴ 37 : 500 = 7.4%
Question 7 Maharashtra Board Solution
Write the ratio of first quantity to second quantity in the reduced form. i. 1024 MB, 1.2 GB [(1024 MB = 1GB)] ii. ₹ 17, ₹ 25 and 60 paise iii. 5 dozen, 120 units iv. 4 sq.m, 800 sq.cm v. 1.5 kg, 2500 gm
Solution & Step-by-Step Answer:
i. 1024 MB, 1.2 GB 1024 MB = 1 GB

ii. ₹ 17, ₹ 25 and 60 paise
₹ 17 = 17 x 100 paise = 1700 paise
₹ 25 and 60 paise = (25x 100) paise + 60 paise
= (2500 + 60) paise
= 2560 paise

iii. 5 dozen, 120 units
5 dozen = 5 x 12 units = 60 units

iv. 4 sq.m, 800 sq.cm
4 sq.m = 4 x 10000 sq.cm = 40000 sq.cm

v. 1.5 kg, 2500 gm
1.5 kg = 1.5 x 1000 gm = 1500gm

Question 8 Maharashtra Board Solution
If = , then find the values of the following expressions.
Solution & Step-by-Step Answer:
Question 9 Maharashtra Board Solution
If a, b, c, d are in proportion, then prove that
Solution & Step-by-Step Answer:
a, b, c are in continued proportion. …[Given]
Question 10 Maharashtra Board Solution
If a, b, c are ¡n continued proportion, then prove that
Solution & Step-by-Step Answer:
a, b, c are in continued proportion. … [Given] ∴ = Let = = k ∴ b = ck ∴ a = bk = (ck)k... [From (j)] a = ck2 …(ii)
Question 11 Maharashtra Board Solution
Solve:
Solution & Step-by-Step Answer:
∴ 29(2x + 3) = 21 (3x + 2) ∴ 5 + 87= 63x + 42 ∴ 87 – 42 = 63x – 58x ∴ 45 = 5x ∴ x = 9 ∴ x = 9 is the solution of the given equation.
Question 12 Maharashtra Board Solution
If ,then prove that every ratio = .
Solution & Step-by-Step Answer:
Question 13 Maharashtra Board Solution
If , then prove
Solution & Step-by-Step Answer:
Question 1 Maharashtra Board Solution
Take 5 pieces of card paper. Write the following statements, one on each paper. a, b, c, d are positive numbers and is given. Which of the above statements are true or false, write at the back of each card, if false explain why. (Textbook pg. no. 70)
Solution & Step-by-Step Answer:
i. True ii. True iii. False Here, numerator and denominator are multiplied by two different numbers a and b. iv. False Here, different numbers a and b are subtracted from numerator and denominator. v. True

Question 2. In the following activity, the values of a and b can be changed. That is by changing a : b we can create many examples. Teachers should give lot of practice to the students and encourage them to construct their own examples. (Textbook pg. no. 70)

Question 3. Observe the political map of India from a Geography text book. Study the scale of this map. From the given scale find the straight line distances between various cities like i. New Delhi to Bengaluru ii. Mumbai to Kolkata iii. Jaipur to Bhuvaneshvar. (Textbook pg. no. 77) [Students should attempt the above activity on their own.]

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Chapter 4 Ratio and Proportion Practice Set 4.5
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Chapter 5 Linear Equations in Two Variables Practice Set 5.1