SCERT AP 7th Class Maths Solutions Pdf Chapter 7 Ratio and Proportion Review Exercise Questions and Answers.

## AP State Syllabus 7th Class Maths Solutions 7th Lesson Ratio and Proportion Review Exercise

Question 1.

Find the ratio of the following:

(i) 5,8

Answer:

5 : 8

(ii) ₹ 10, ₹ 15

Answer:

10 : 15

2 : 3

∴ ₹ 10 : ₹15 = 2 : 3

(iii) 25 kg., 20. kg.

Answer:

25 kg : 20 kg

25 : 20

5 : 4

∴ 25 kg : 20 kg = 5 : 4

(iv) 5l, 500ml

Answer:

5l : 500 ml

5000 ml: 500 ml (∵ 1l = 1000 ml, 5l = 5000 ml)

5000 : 500

10 : 1

∴ 5l : 500 ml = 10 : 1

(v) 2 km. 500 m, 1 km. 750 m

Answer:

2 km. 500 m : 1 km. 750 m

2000 m + 500 m : 1000 m + 750 m (∵ 1 km = 1000m; 2 km = 2000 m)

2500 : 1750

10 : 7 (∵ HCF = 25)

∴ 2 km. 500 m : 1 km. 750 m = 10 : 7

(vi) 3 hrs, 1 hr. 30 min.

Answer:

3 hrs : 1 hr. 30 min

3 × 60 : (1 × 60) + 30 (∵ 1 hr = 60 min; 3h = 3 × 60 = 180 min)

180 min : 60 + 30 min

2 : 1

∴ 3 hrs : 1 hr. 30 min = 2:1

(vii) 40 days, 1 year

Answer:

40 days : 1 year

40 days : 365 days (∵ 1 year = 365 days)

40 : 365 (∵ HCF = 5)

8 : 73

∴ 40 days : 1 year = 8 : 73

(Or)

40 days : 366 days (∵ 1 year = 366 days for leap year)

20 : 183 (∵ HCF = 2)

Question 2.

Express the following ratios in the simplest form:

(i) 120 : 130

Answer:

Given 120 : 130

12 : 13

∴ 120 : 130 = 12 : 13

(ii) 135:90

Answer:

Given 135 : 90

27 : 18

3 : 2

∴ 135 : 90 = 3 : 2

(iii) 48 : 144

Answer:

Given 48: 144

12 : 36

1 : 3

∴ 48 : 144 = 1:3

(iv) 81 : 54

Answer:

Given 81 : 54

9 : 6

3 : 2

∴ 81 : 54 = 3 : 2

(v) 432 : 378

Answer:

Given 432 : 378

216 : 189

24 : 21

8 : 7

∴ 432 : 378 = 8 : 7

Question 3.

Check whether the two ratios given below are in proportion.

(i) 10 : 20, 25 : 50

Answer:

Given 10 : 20, 25 : 50

a :b = 10 : 20

So, a : b = 1 : 2

c : d = 25 : 50

also, c : d = 1 : 2

If a : b = c: d, then a, b, c, d are in proportion.

a : b = c : d = 1 : 2

Therefore, 10 : 20, 25 : 50 are in proportion.

(ii) 18 : 12, 15 : 10

Answer:

Given 18 : 12, 15 : 10

a : b = 18 : 12

= 6 : 4

c : d = 15 : 10

also c : d = 3 : 2

So, a : b = 3 : 2

If a : b = c : d, then a, b, c, d are in proportion.

a : b = c : d = 3 : 2

Therefore, 18 : 12, 15 : 10 are in proportion.

(iii) 25 : 20, 16 : 14

Answer:

Given 25 : 20, 16 : 14

a : b = 25 : 20

So, a : b = 5 : 4

5 : 4 ≠ 8 : 7

∴ a : b ≠ c : d

c : d = 16 : 14

c : d = 8 : 7

If a : b = c : d, then a, b, c, dare in propottion.

Here a : b ≠ c : d

So, a, b, c, d are not in proportion.

(iv) 54 : 27, 18 : 9

Answer:

Given 54 : 27, 18 : 9

a : b = 54 : 27.

= 6 : 3

So, a : b = 2 : 1

c : d = 18 : 9

also, c : d = 2 : 1

If a : b = c : d, then a, b, c, d are in proportion.

a : b = c : d = 2 : 1

Therefore, 54: 27, 18 : 9 are in proportion.

Question 4.

Find the missing number in each of the following problems:

(i) 15 : 19 = 45 : _______

Answer:

Given 15 : 19 = 45 : x

Let the missing term be ‘x’.

If a : b = c : d, then a, b, c and d are in proportion, then the product of extremes is equal to the product of means that is a . d = b . c

⇒ 15 × x = 19 × 45

⇒ x = 19 × 3

∴ x = 57

(ii) 9 : 13 = ____ : 65

Answer:

Given 9 : 13 = x : 65

Let the missing term be ‘x’.

If a : b = c : d, then a, b, c and d are in proportion, then the product of extremes is equal to the product of means that is a . d = b . c

⇒ 9 × 65 = 13 × x

⇒ 45 = x

∴ x = 45

(iii) 8 : ______ = 72 : 63

Answer:

Given 8 : x = 72 : 63

Let the missing term be ‘x’.

If a : b = c : d, then a, b, c and d are in proportion, then the product of extre¬mes is equal to the product of means that is a . d = b . c

⇒ 8 × 63 = x × 72

⇒ 7 = x

∴ x = 7

Question 5.

Fill in the boxes with equivalent ratio of 3 : 4.

Answer:

Given a : b = 3 : 4 (or) \(\frac{3}{4}\)

\(\frac{a}{b}=\frac{3}{4}\)

Equivalent ratios

Therefore, a : b = 3 : 4 = 6 : 8

= 9 : 12 = 12 : 16 = 15 : 20 = 18 : 24

Question 6.

Pick out any four numbers from below and arrange them so that they are in proportion 2, 3, 10, 12> 15, 18.

Ex : 2 : 10 = 3 : 15

(i) : __________

Answer:

2 : 3; 12 : 18

a : b = 2 : 3, c : d = 12: 18

If a, b, C, d are in proportion, then the product of extremes is equal to the pro¬duct of means.

a . d = b . c

2 × 18 = 3 × 12

36 = 36

So, 2 : 3 = 12 : 18

(ii) : __________

Answer:

10 : 12 = 15 : 18

a : b = 10 : 12

c : d = 15 : 18

If a, b, c, d are in proportion, then the product of extremes is equal to the product of means.

a . d = b . c

10 × 18 = 15 × 12

180 = 180

So, 10 : 12 = 15 : 18

Question 7.

Divide ₹ 1500 into two parts such that they are in the ratio of 7 : 3.

Answer:

Given amount to be divide = ₹ 1500 .

Ratio to be divide = 7:3

Sum of the terms in the ratio = 7 + 3 = 10

[Or 1500 – 1050 = 450]

Question 8.

If there are 20 chocolates in a packet, Rajani and Ragini share them and Rajani takes 12 chocolates, then what is the ratio of chocolates taken by Rajani to Ragini?

Answer:

Total number of Chocolates = 20

Number of chocolates Rajani taken = 12

Number of chocolates Ragini taken = 20 – 12 = 8

Ratio of Rajani to Ragini = 12 : 8

Ratio of chocolates taken by Rajani to Ragini = 3 : 2

Question 9.

A pipe is cut into two parts in such a ratio that the first part to second part is 7:8. If the length of the 2nd part is 48cm, then what is the length of the first part? What is the total length of the pipe before cutting?

Answer:

Given ratio of two parts of pipe = 7:8

Length of the second part = 48 cm

Length of the first part = x cm

Ratio of the two parts = x : 48

Product of extremes = Product of means

⇒ 8 × x = 48 × 7

⇒ x = 42

∴ Length of first part of the pipe = x = 42 cm

Length of the pipe = 42 + 48 = 90 cm