## 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