ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 6 Ratio and Proportion Check Your Progress
Question 1.
A rectangular park is 120 m long and 75 m wide. Find the ratio of:
(i) breadth to its length
(ii) length to its perimeter
Solution:
Length of park (l) = 120 m and width (b) = 75 m
Perimeter = 2(l + b) = 2(120 + 75) m = 2 × 195 = 390 m
(i) Ratio between breadth to length = 75 : 120 = 5 : 8 (Dividing by 15)
(ii) Ratio between length to perimeter = 120 : 390 = 4 : 13 (Dividing by 30)
Question 2.
Divide the angles of a triangle in the ratio 2 : 3 : 4.
Solution:
Given ratio = 2 : 3 : 4
Sum of the terms of ratio = 2 + 3 + 4 = 9
Sum of angles of a triangle = 180°
Thus, we are to divide 180° in the ratio 2 : 3 : 4
Question 3.
Heights of Anshul, Ankita and Dhruv are 1.04 m, 1.30 m and 91 cm respectively. Divide 100 sweets among them in the ratio of their heights.
Solution:
Height of Anshul = 1.04 m = (1.04 × 100) cm = 104 cm
Height of Ankita = 1.30 m = (1.30 × 100) cm = 130 cm
Height of Dhruv = 91 cm
Ratio of their heights = 104 cm : 130 cm : 91 cm
= 104 : 130 : 91
= 8 : 10 : 7 (Dividing each by 13)
We are to divide 100 sweets in the ratio 8 : 10 : 7.
Sum of the terms of the ratio = 8 + 10 + 7 = 25
Question 4.
The weights of Divya and Himanshu are in the ratio 5 : 7. If Himanshu weighs 28 kg, find the weight of Divya.
Solution:
Let the weight of Divya = x
Then the ratio of the weight of Divya and Himanshu will be x : 28 kg
According to the given statement
x : 28 :: 5 : 7
By cross product rule
Product of extremes = Product of means
x × 7 = (28 × 5) kg
x = 20 kg
Weight of Divya = 20 kg
Question 5.
Which ratio is smaller- 9 : 13 or 7 : 11 ?
Solution:
9 : 13 = \(\frac { 9 }{ 11 }\) and 7 : 11 = \(\frac { 7 }{ 11 }\)
Converting them into equivalent like fraction
by taking L.C.M. of 13 and 11 = 143
Question 6.
Find the fourth proportional to
(i) 4, 7, 20
(ii) 2\(\frac { 1 }{ 2 }\), 1\(\frac { 1 }{ 4 }\), 2.2
Solution:
(i) 4, 7, 20
Let the fourth proportional be x, then
4, 7, 20, x are in proportion
4 : 7 :: 20 : x
Using cross product rule
Product of extremes = Product of means
4 × x = 7 × 20
x = 35
(ii) 2\(\frac { 1 }{ 2 }\), 1\(\frac { 1 }{ 4 }\), 2.2
= \(\frac { 5 }{ 2 }\) , \(\frac { 5 }{ 4 }\) , 2.2
Let the fourth proportional be x, then
\(\frac { 5 }{ 2 }\) , \(\frac { 5 }{ 4 }\) , 2.2, x are in proportion
\(\frac { 5 }{ 2 }\) : \(\frac { 5 }{ 4 }\) :: 2.2 : x
Using cross product rule
Product of extremes = Product of means
Question 7.
A typist types 70 pages in 3 hours 30 minutes. How long will she take to type 300 pages?
Solution:
A typist types 70 pages in 3 hours 30 minutes
Question 8.
12 looms weave 210 m cloth per day. How many metres of cloth will 8 looms weave per day?
Solution:
12 looms weave 210 m cloth per day
Let 8 looms weave per day = x m
12 : 8 = 210 : x
12 × x = 8 × 210 (ad = bc)
x = 140 m
They will weave 140 m of cloth.
Question 9.
A journey takes 4 hours 30 minutes at a speed of 60 km/h. How long will the same journey take at a speed of 15 m/sec?
Solution:
A journey takes 4 hours 30 minutes
= 4\(\frac { 1 }{ 2 }\) = \(\frac { 9 }{ 2 }\) h at a speed of 60 km/h
If speed is 15 m/sec
Convert m/s into km/h
