Practice Set 4.1 Algebra 9th Std Maths Part 1 Answers Chapter 4 Ratio and Proportion
Question 1
Maharashtra Board Solution
From the following pairs of numbers, find the reduced form of ratio of first number to second number. i. 72,60 ii. 38,57 iii. 52,78
Solution & Step-by-Step Answer:
i. 72, 60
ii. 38, 57
iii. 52, 78
Question 2
Maharashtra Board Solution
Find the reduced form of the ratio of the first quantity to second quantity. i. ₹ 700, ₹ 308 ii. ₹ 14, ₹ 12 and 40 paise iii. 5 litres, 2500 ml iv. 3 years 4 months, 5 years 8 months v. 3.8 kg, 1900 gm vi. 7 minutes 20 seconds, 5 minutes 6 seconds
Solution & Step-by-Step Answer:
i. ₹ 700, ₹ 308
ii. ₹ 14, ₹12 and 40 paise
₹ 14 = 14 x 100 paise = 1400 paise
₹ 12 and 40 paise = 12 x 100 paise + 40 paise
= (1200 + 40) paise
= 1240 paise
iii. 5 litres, 2500 ml
5 litres = 5 x 1000 ml = 5000ml
iv. 3 years 4 months, 5 years 8 months
3 years 4 months = 3×12 months + 4 months
= (36 + 4) months
= 40 months
5 years 8 months = 5 x 12 months + 8 months
= (60 + 8) months
= 68 months
v. 3.8 kg, 1900 gm
3.8 kg = 3.8 x 1000 gm = 3800 gm
vi. 7 minutes 20 seconds, 5 minutes 6 seconds
7 minutes 20 seconds = 7 x 60 seconds + 20 seconds
= (420 + 20) seconds
= 440 seconds
5 minutes 6 seconds = 5 x 60 seconds + 6 seconds
= (300 + 6) seconds
= 306 seconds
Question 3
Maharashtra Board Solution
Express the following percentages as ratios i. 75 : 100 ii. 44 : 100 iii. 6.25% iv. 52: 100 v. 0.64%
Solution & Step-by-Step Answer:
Question 4
Maharashtra Board Solution
Three persons can build a small house in 8 days. To build the same house in 6 days, how many persons are required?
Solution & Step-by-Step Answer:
Let the persons required to build a house in 6 days be x. Days required to build a house and number of persons are in inverse proportion. ∴ 6 × x = 8 × 3 ∴ 6 x = 24 ∴ x = 4 ∴ 4 persons are required to build the house in 6 days.
Question 5
Maharashtra Board Solution
Convert the following ratios into percentages. i. 15 : 25 ii. 47 : 50 iii. iv. v.
Solution & Step-by-Step Answer:
Let 15 : 25 = x % ∴ 15 : 25 = 60 %
ii. Let 47 : 50 = x%
∴ 47 : 50 = 94 %
iii. Let = x %
iv. Let = x %
v. Let = x %
Question 6
Maharashtra Board Solution
The ratio of ages of Abha and her mother is 2 : 5. At the time of Abha’s birth her mothers age was 27 years. Find the present ages of Abha and her mother.
Solution & Step-by-Step Answer:
The ratio of ages of Abha and her mother is 2 : 5. Let the common multiple be x. ∴ Present age of Abha = 2x years and Present age of Abha’s mother = 5x years According to the given condition, the age of Abha’s mother at the time of Abha’s birth = 27 years ∴ 5x – 2x = 27 ∴ 3x = 27 ∴ x = 9 ∴ Present age of Abha = 2x = 2 x 9 = 18 years ∴ Present age of Abha’s mother = 5x =5 x 9 = 45 years The present ages of Abha and her mother are 18 years and 45 years respectively.
Question 7
Maharashtra Board Solution
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?
Solution & Step-by-Step Answer:
Present age of Vatsala = 14 years Present age of Sara = 10 years After x years, Vatsala’s age = (14 + x) years Sara’s age = (10 + x) years According to the given condition, After x years the ratio of their ages will become 5 : 4 ∴ = ∴ 4(14 + x) = 5(10 + x) ∴ 56 + 4x = 50 + 5x ∴ 56 – 50 = 5x – 4x ∴ 6 = x ∴ x = 6 ∴ After 6 years, the ratio of their ages will become 5 : 4.
Question 8
Maharashtra Board Solution
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 ?
Solution & Step-by-Step Answer:
The ratio of present ages of Rehana and her mother is 2 : 7 Let the common multiple be x. ∴ Present age of Rehana = 2x years and Present age of Rehana’s mother = 7x years After 2 years, Rehana’s age = (2x + 2) years Age of Rehana’s mother = (7x + 2) years According to the given condition, After 2 years, the ratio of their ages will be 1 : 3 ∴ = ∴ 3(2x + 2) = 1(7x + 2) ∴ 6x + 6 = 7x + 2 ∴ 6 – 2 = 7x – 6x ∴ 4 = x ∴ x = 4 ∴ Rehana’s present age = 2x = 2 x 4 = 8 years ∴ Rehana’s present age is 8 years.