Exercise 7
(1) Choose the correct option:
(i) What is the ratio of the proportion 5 : 7?
(ii) What is the simplest form of
60
36
?
(iii) What is the ratio of 2 kg to 800 grams?
Ans.
(i) (a)
5
7
(ii) (d)
5
3
(iii) (c)
5
2
(2)
In a class of 45 students, 15 students play hockey, 20 students play kabaddi
and the remaining students play kho-kho. If each student plays only one game,
solve the following questions.
i) Find the ratio of number of students playing hockey to number of students playing kho-kho.
ii) Find the ratio of number of students playing Kabaddi to the total number of students.
iii) Find the ratio of number of students playing hockey to the total number of students.
Solution
Total students = 45
Number of students playing hockey = 15
Number of students playing kabaddi = 20
Students playing kho-kho = 45 − (15 + 20) = 45 − 35 = 10
(i)
Ratio of student playing hockey to students playing kho-kho
= 15 : 10
=
15
10
=
15 ÷ 5
10 ÷ 5
=
3
2
= 3 : 2
Ans. 3 : 2 or
3
2
(ii)
Ratio of students playing kabaddi to total number of students
= 20 : 45
=
20
45
=
20 ÷ 5
45 ÷ 5
=
4
9
= 4 : 9
Ans. 4 : 9 or
4
9
(iii)
Ratio of students playing hockey to total number of students
= 15 : 45
=
15
45
=
15 ÷ 5
45 ÷ 5
=
3
9
=
1
3
= 1 : 3
Ans. 1 : 3 or
1
3
Ans. The required ratios are:
(i) 3 : 2,
(ii) 4 : 9,
(iii) 1 : 3.
(3)
Colour any three squares in the adjacent figure with the colour of your choice
and write the answers to the following questions.
Figure
i) The ratio of the number of squares you have coloured to the total number of squares = …
ii) Ratio of number of uncoloured squares to total number of squares = …
iii) Ratio of number of coloured squares to number of uncoloured squares = …
Solution
Coloured figure
i)
The ratio of the number of squares you have coloured to the total number of squares
=
3
10
ii)
Ratio of number of uncoloured squares to total number of squares
=
7
10
iii)
Ratio of number of coloured squares to number of uncoloured squares
=
3
7
(4)
The length of a rectangular sheet is 1.20 m and the width is 48 cm.
Find the ratio of the width to the length of the sheet.
Solution
The length of the rectangular sheet = 1.20 m = 120 cm.
Width of the sheet = 48 cm.
The ratio of 48 cm to 1.20 m means the ratio of 48 cm to 120 cm.
∴
48 cm
120 cm
=
48
120
=
48 ÷ 24
120 ÷ 24
=
2
5
= 2 : 5
Ans. The ratio of the width to the length of the sheet = 2 : 5
or
2
5
.
(5)
Michael's monthly income of ₹52,000 out of which he saves ₹3,000 monthly.
Then find the ratio of his monthly income to his expenditure.
Solution
Michael's monthly income = ₹52,000; His monthly savings = ₹3,000.
∴ his monthly expenditure = ₹52,000 − ₹3,000 = ₹49,000.
The ratio of Michael's monthly income to his expenditure
= 52,000 : 49,000
=
52000
49000
=
52
49
= 52 : 49
Ans. The ratio of Michael's monthly income to his expenditure = 52 : 49
or
52
49
.
(6)
A school wanted to purchase 50 saplings for planting trees on the occasion of
Environment Day. The school purchased 35 saplings from 'Yashoda' nursery
for ₹ 455 and the remaining saplings from 'Amol' nursery for ₹240.
From which nursery will the school get the saplings purchased at low price?
Solution
Total saplings = 50
Saplings purchased from 'Yashoda' nursery = 35
∴ saplings purchased from 'Amol' nursery
= 50 − 35 = 15.
(i) Let us find cost of 1 sapling from 'Yashoda' nursery.
Cost of 35 saplings = ₹ 455
∴ cost of 1 sapling = ₹ 455 ÷ 35 = ₹ 13
(ii) Let us find cost of 1 sapling from 'Amol' nursery.
Cost of 15 saplings = ₹ 240
∴ cost of 1 sapling = ₹ 240 ÷ 15 = ₹ 16
The cost of 1 sapling from 'Yashoda' nursery is less than
the cost of 1 sapling from 'Amol' nursery.
Ans. The school will get saplings at low price from
'Yashoda' nursery.
(7)
A cook prepares 10 kilograms of rice every day for 100 students in a school
as part of mid-day meal. But one day, due to heavy rain, only 80 students
were present in the school. How many kilograms of rice should be cooked on
that day?
Solution
100 students need 10 kg of rice everyday.
(10 kg = 10000 g)
∴ rice needed for 1 student
= 10000 ÷ 100
= 100 g
∴ rice needed for 80 students
= 100 × 80
= 8000 g
8000 g = 8 kg
Ans. 8 kg of rice will be needed for 80 students.