## RS Aggarwal Class 7 solutions of Chapter 8 Ratio and Proportion Ex 8A in pdf free download

**Question 1.****Express each of the following ratios in the simplest form : ‘****(i) 24 : 40****(ii) 13.5 : 15****(iii) 6 : 7****(iv)
**

**:**

**(v) 4 : 5 :**

**(vi) 2.5 : 6.5 : 8**

**Solution:**

(i) 24 : 40

HCF of 24, 40 = 8

24 : 40 = 24 ÷ 8 : 40 ÷ 8 = 3 : 5 (Dividing by 8)

(ii) 13.5 : 15 or 135 : 150

HCF of 135 and 150 = 15

135 ÷ 15 : 150 ÷ 15 (Dividing by 15)

= 9 : 10

HCF of 25, 65, 80 = 5

Dividing by 5,

5 : 13 : 16

**Question 2.****Express each of the following ratios in the simplest form :****(i) 75 paise : 3 rupees****(ii) 1 m 5 cm : 63 cm****(iii) 1 hour 5 minutes : 45 minutes****(iv) 8 months : 1 year****(v) (2 kg 250 g) : (3 kg)****(vi) 1 km : 750 m****Solution:**

(i) 75 paise : 3 rupees = 75 paise : 300 paise

(converting into same kind)

HCF of 75, 300 = 75

75 : 300 = 75 ÷ 75 : 300 ÷ 75 (Dividing by 75) = 1 : 4

(ii) 1 m 5 cm : 63 cm = 105 cm : 63 cm

(converting into same kind)

HCF of 105 and 63 = 21

105 ÷ 21 : 63 ÷ 21 (Dividing by 21)

= 5 : 3

(iii) 1 hour 5 minutes : 45 minutes = 65 minutes : 45 minutes

(converting into minutes)

13 : 9 (dividing by 5)

= 13 : 9

(iv) 8 months : 1 year = 8 months : 12 months

(converting into the same kind)

HCF of 8 and 12 = 4

Dividing by 4

8 ÷ 4 : 12 ÷ 4

= 2 : 3

(v) 2 kg 250 g : 3 kg = 2250 g : 3000 g (converting into the same kind)

HCF of 2250 and 3000 = 750

Dividing by 750,

2250 ÷ 750 : 3000 ÷ 750 = 3 : 4

(vi) 1 km : 750 m = 1000 m : 750 m

(converting into metre)

= 4 : 3 (dividing by 250)

= 4 : 3

**Question 3.****If A : B = 7 : 5 and B : C = 9 : 14, find A : C.****Solution:**

**Question 4.****If A : B = 5 : 8 and B : C = 16 : 25, find A : C.****Solution:**

A : B = 5 : 8, B : C = 16 : 25

**Question 5.****If A : B = 3 : 5, B : C = 10 : 13, find A : B : C.****Solution:**

A : B = 3 : 5, B : C = 10 : 13

A : B : C = 6 : 10 : 13

**Question 6.****If A : B = 5 : 6, and B : C = 4 : 7, find A : B : C.****Solution:**

A : B = 5 : 6 and B : C = 4 : 7

**Question 7.****Divide Rs. 360 between Kunal and Mohit in the ratio 7 : 8****Solution:**

Total amount = Rs. 360

Sum of ratios = 7 + 8 = 15

**Question 8.****Divide Rs. 880 between Rajan and Kamal in the ratio : ****Solution:**

Total amount = Rs. 880

**Question 9.****Divide Rs. 5600 between A, B and C in the ratio 1 : 3 : 4.****Solution:**

Total amount = Rs. 5600

Ratio in A : B : C = 1 : 3 : 4

**Question 10.****What number must be added to each term of the ratio 9 : 16 to make the ratio 2 : 3?****Solution:**

Let x be added to each term Then

9 + x : 16 + x = 2 : 3

**Question 11.****What number must be subtracted from each term of the ratio 17 : 33 so that the ratio becomes 7 : 15?****Solution:**

Let x be subtracted from each term Then

(17 – x) : (33 – x) = 7 : 15

**Question 12.****Two numbers are in the ratio 7 : 11. If 7 is added to each of the numbers, the ratio becomes 2 : 3. Find the numbers.****Solution:**

Ratio in two numbers = 7 : 11

Let first number = 7x

Then second number = 11x

Then adding 7 to each number, the ratio is 2 : 3

=

By cross multiplying:

3 (7x + 7) = 2 (11x + 7)

⇒ 21x + 21 = 22x + 14

⇒ 21 – 14 = 22x – 21x

⇒ x = 7

First number = 7x = 7 x 7 = 49

and second number = 11x = 11 x 7 = 77

Hence numbers are 49, 77

**Question 13.****Two numbers are in the ratio 5 : 9. On subtracting 3 from each, the ratio becomes 1 : 2. Find the numbers.****Solution:**

The ratio in two numbers = 5 : 9

Let the first number = 5x

Then second number = 9x

By subtracting 3 from each number the ratio is 1 : 2

=

By cross multiplication,

2 (5x – 3) = 1 (9x – 3)

⇒ 10x – 6 = 9x – 3

⇒ 10x – 9x = -3 + 6

⇒ x = 3

First number = 5x = 5 x 3 = 15

and second .number = 9x = 9 x 3 = 27

Hence numbers are 15, 27

**Question 14.****Two numbers are in the ratio 3 : 4. If their LCM is 180, find the numbers.****Solution:**

Ratio in two numbers = 3 : 4

LCM = 180

Let first number = 3x

Then second number = 4x

Now LCM = 3 x 4 x x = 12x

12x = 180

⇒ x = 15

Numbers will be 3 x 15 = 45 and 4 x 15 = 60

**Question 15.****The ages of A and B are in the ratio 8 : 3. Six years hence, their ages will be in the ratio 9 : 4. Find their present age.****Solution:**

Ratio in present ages of A and B = 8 : 3

Let A’s age = 8x

Then B’s age = 3x

6 years hence,

A’s age will be = 8x + 6

and B’s will be = 3x + 6

=

(By cross multiplication)

4 (8x + 6) = 9 (3x + 6)

⇒ 32x + 24 = 27x + 54

⇒ 32x – 27x = 54 – 24

⇒ 5x = 30

⇒ x = 6

A’s present age = 8x = 8 x 6 = 48 years

and B’s age = 3x = 3 x 6 = 18 years

**Question 16.****The ratio of copper and zinc in an alloy is 9 : 5. If the weight of copper in the alloy is 48.6 grams, find the weight of zinc in the alloy.****Solution:**

Ratio in copper and zinc = 9 : 5

Let alloy = x gm

**Question 17.****The ratio of boys and girls in a school is 8 : 3. If the total number of girls be 375, find the number of boys in the school.****Solution:**

Ratio in boys and girls = 8 : 3

and total number of girls = 375

Let number of boys = 8x

Then number of girls = 3x

3x = 375

⇒ x = 125

Number of boys = 8x = 8 x 125 = 1000

**Question 18.****The ratio of monthly income to the savings of a family is 11 : 2. If the savings be Rs. 2500, find the income and expenditure.****Solution:**

Ratio in income and savings = 11 : 2

Let income = 11x

Then savings = 2x

But savings = Rs. 2500

2x = 2500

⇒ x = 1250

Then income = 1250 x 11 = Rs. 13750

and expenditure = Total income – savings = 13750 – 2500 = Rs. 11250

**Question 19.****A bag contains Rs. 750 in the form of rupee, 50P and 25P coins in the ratio 5 : 8 : 4. Find the number of coins of each type.****Solution:**

Total amount = Rs. 750

Ratio in rupee, 50 P and 25 P coins =5 : 8 : 4

Let number of rupees = 5x

Number of 50 P coins = 8x

and number of 25 coins = 4x

According to the condition,

Number of 1 Re coins = 5x = 5 x 75 = 375

Number of 50 P coins = 8x = 8 x 75 = 600

and number of 25 P coins = 4x = 4 x 75 = 300

**Question 20.****If (4x + 5) : (3x + 11) = 13 : 17, find the value of x.****Solution:**

(4x + 5) : (3x + 11) = 13 : 17

=

By cross multiplication,

68x + 85 = 39x + 143

⇒ 68x – 39x = 143 – 85

⇒ 29x = 58

x = 2

Hence x = 2

**Question 21.****If x : y = 3 : 4, find (3x + 4y) : (5x + 6y).****Solution:**

x : y = 3 : 4

**Question 22.****If x : y = 6 : 11, find (8x – 3y) : (3x + 2y).****Solution:**

x : y = 6 : 11

=

Now (8x – 3y) : (3x + 2y)

**Question 23.****Two numbers are in the ratio 5 : 7. If the sum of the numbers is 720, find the numbers.****Solution:**

Sum of two numbers = 720

Ratio of two numbers = 5 : 7

Let first number = 5x

Then second number = 7x

5x + 7x = 720

⇒ 12x = 720

⇒ x = 60

First number = 5x = 5 x 60 = 300

and second number = 7x = 7 x 60 = 420

**Question 24.****Which ratio is greater :****(i) (5 : 6) or (7 : 9)****(ii) (2 : 3) or (4 : 7)****(iii) (1 : 2) or (4 : 7)****(iv) (3 : 5) or (8 : 13)****Solution:**

(i) (5 : 6) or (7 : 9)

**Question 25.****Arrange the following ratios in ascending order:****(i) (5 : 6), (8 : 9), (11 : 18)****(ii) (11 : 14), (17 : 21), (5 : 7) and (2 : 3)****Solution:**

(i) (5 : 6), (8 : 9), (11 : 18)

## Leave a Reply