ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 8 Ratio and Proportion Check Your Progress

Question 1.
From the given figure, find the ratio of
ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 8 Ratio and Proportion Check Your Progress 1
(i) Number of triangles to the number of circles inside the rectangle.
(ii) Number of squares to the number of all the figures inside the rectangle.
(iii) Number of circles to the number of remaining figures inside the rectangle.
Solution:
Number of triangles = 3
Number of rectangles = 2
Number of circles = 2
(i) 3 : 2
(ii) 2 : 7
(iii) 2 : 5

Question 2.
The length of a pencil is 16 cm and its diameter is 6 mm. What is the ratio of the diameter of the pencil to that of its length?
Solution:
Length of a pencil = 16 cm = 16 cm × 10 = 160 mm
Diameter of the pencil = 6 mm
Ratio of the diameter of the pencil to that of its length = 6 : 160 = 3 : 80

Question 3.
A certain club has 100 members, out of which 25 play tennis, 28 play badminton, 12 play chess and the rest do not play any game. Find the ratio of number of members who play
(i) badminton to the number of those who play chess.
(ii) badminton to the number of those who do not play any game.
(iii) tennis to the number of those who do not play any game.
(iv) tennis to the number of those who play either badminton or chess.
Solution:
Total number of members = 100
Members who plays tennis = 25
Members who plays badminton = 28
Members who plays chess = 12
Members who play nothing = 100 – (25 + 28 + 12)
= 35
(i) 28 : 12 = 7 : 3
(ii) 28 : 35 = 4 : 5
(iii) 25 : 28 = 5 : 7
(iv) 25 : 40 = 5 : 8

Question 4.
Do the ratios 15 cm to 3 m and 25 seconds to 3 minutes from a proportion?
Solution:
Given, first ratio = 15 cm : 3 m
= 15 cm : 300 cm
= 1 : 20
and second ratio = 25 seconds : 3 minutes
= 25 seconds : 3 × 60 seconds
= 25 : 180 = 1 : 6
No, they do not form proportion.

Question 5.
Divide ₹500 among Suresh and Awanti in the ratio 3 : 7.
Solution:
Total amount = ₹500
Ratio = 3 : 7
Sum of ratios = 3 + 7=10
Suresh shares = ₹\(\frac{500 \times 3}{10}\) = ₹150
Awanti shares = ₹ \(\frac{500 \times 7}{10}\) = ₹350

Question 6.
The ratio of the number of girls to that of boys in a school is 9 : 11. If the number of boys in the school is 2035, find:
(i) the number of girls in the school,
(ii) the number of students in the school.
Solution:
Let the number of girls = x
Girls : Boys = 9 : 11
No. of boys = 2035
x : 2035 = 9 : 11
ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 8 Ratio and Proportion Check Your Progress 2
No. of girls = 1665.
(ii) Total students in school = No. of boys + No. of girls
2035 + 1665 = 3700

Question 7.
The ratio of income to expenditure of a family is 7 : 6. Find the savings if the income of family is ₹42000.
Solution:
Ratio in income and expenditure = 7 : 6
Total income = ₹42000
Let expenditure = x, then
7 : 6 :: 42000 : x
⇒ \(x=\frac{6 \times 42000}{7}\) = ₹36000
Now,
Income = ₹42000
Expenditure = ₹36000
∴ Savings = Income – Expenditure
= ₹(42000 – 36000) = ₹6000

Question 8.
An employee earns ₹72,000 in 3 months.
(i) How much does he earn in 7 months?
(ii) In how many months will he earn ₹3,60,000?
Solution:
(i) ∵ Earning in 3 months = ₹72000
∴ Earning in 1 month = ₹\(\frac{72000}{3}\) = 24000
Earning in 7 months = ₹24000 × 7
= ₹1,68,000
(ii) ₹24000 is earned in = 1 month
₹1 is earned is = \(\frac{1}{24000}\)
₹3,60,000 is earned in
ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 8 Ratio and Proportion Check Your Progress 3

Question 9.
A train travels 110 km in 2 hours and a car travels 245 km in \(3 \frac{1}{2}\) hours. What is the ratio of the speed of the train to that of the car?
Solution:
A train travels in 2 hours =110 km
It will cover in 1 hour = \(\frac{110}{2}\) = 55 km
A car travel in \(\frac{7}{2}\) hours = 245 km
∴ It will cover in 1 hour =\(\frac{2 \times 245}{7}\) = 70 km
Ratios in their speed = 55 : 70 = 11 : 14

ML Aggarwal Class 6 Solutions for ICSE Maths

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