ML Aggarwal Ratio and Proportion Exe-8.1 Class 6 ICSE Maths Solutions. We Provide Step by Step Answer of Exe-8.1 Questions for Ratio and Proportion as council prescribe guideline for upcoming board exam. Visit official Website CISCE for detail information about ICSE Board Class-6.

## ML Aggarwal Ratio and Proportion Exe-8.1 Class 6 ICSE Maths Solutions

Board | ICSE |

Publications | Avichal Publishig Company (APC) |

Subject | Maths |

Class | 6th |

Chapter-8 | Ratio and Proportion |

Writer | ML Aggarwal |

Book Name | Understanding |

Topics | Solution of Exe-8.1 Questions |

Edition | 2023-2024 |

**Ratio and Proportion Exe-8.1**

**ML Aggarwal Class 6 ICSE Maths Solutions**

Page-160

**Question 1. Express the following ratios in simplest form:**

(i) 20 : 40

(ii)40 : 20

(iii) 81 : 108

(iv) 98 : 63

**Answer:**

(i) 20 : 40 = 20/40 = ½ = 1 : 2

(ii) 40 : 20 = 40/20 = 2/1 = 2 : 1

(iii) 81 : 108 = 81/108 = 9/12 = ¾ = 3 : 4

(iv) 98 : 63 = 98/63 = 14/9 = 14 : 9

**Question 2. Fill in the missing numbers in the following equivalent ratios:**

**Answer:**

**Question 3. Find the ratio of each of the following in simplest form :**

(i) 2.1 m to 1.2 m

(ii) 91 cm to 1.04m

(iii) 3.5 kg to 250gm

(iv) 60 paise to 4 rupees

(v) 1 minute to 15 seconds

(vi) 15 mm to 2 cm

**Answer:**

**(i) 2.1 m : 1.2 m**

= 2.1/ 1.2

= 21/12 × 10/10

= 7 : 4

**(ii) 91 cm : 1.04mm or (1.04 × 100) cm = 104 cm [As 1 m = 100 cm]**

= 91 cm : 104 cm

= 91/104

= 7 : 8

**(iii) 3.5 kg : 250 gm or (3.5 × 1000) gm : 250 gm [As 1 kg = 1000 gm]**

= 3500 gm : 250 gm

= 3500/250

= 14/1

= 14 : 1

**(iv) 60 paise : 4 rupees or 60 paise : (4 × 100) paise [As 1 Rs = 100 paise]**

= 60 paise : 400 paise

= 60/400

= 6/40

= 3/20

= 3 : 20

**(v) 1 minute : 15 seconds or 60 seconds : 15 seconds [As 1 minute = 60 seconds]**

= 60 : 15

= 60/15

= 4/1

= 4 : 1

**(vi) 15 mm : 2 cm or 15 mm : (2 × 10) mm [As 1 cm = 10 mm]**

= 15 mm : 20 mm

= 15/20

= 3/4

= 3 : 4

**Question 4. The length and the breadth of a rectangular park are 125 m and 60 m respectively. What is the ratio of the length to the breadth of the park?**

**Answer:**

Length of rectangular park = 125 m

Breadth of rectangular park = 60 m

∴ Ratio of the length to the breadth of park is

125/60 = 25/12 = 25 : 12

**Question 5. The population of village is 4800. If the numbers of females is 2160, find the ratio of males to that of females.**

**Answer:**

Population of village = 4800

No. of females = 2160

No. of males = 4800 – 2160 = 2640

No. of males : No. of females

2640 : 2160

= 2640/2160

= 264/216

= 11/9

= 11 : 9

**Question 6. In a class, there are 30 boys and 25 girls. Find the ratio of the numbers of**

(i) boys to that of girls.

(ii) girls to that of total number of students.

(iii) boys to that of total numbers of students.

**Answer:**

Boys = 30, girls = 25

Total students = 30 + 25 = 55

**(i) boys : girls = 30 : 25**

= 30/25 = 6/5 = 6 : 5

**(ii) girls : Total no. of students = 25 : 55**

= 25/55 = 5/11 = 5 : 11

**(iii) Boys : Total no. of students = 30 : 55**

= 30/55 = 6/11 = 6 : 11

**Question 7. In a year, Reena earns ₹ 1,50,000 and saves ₹ 50,000. Find the ratio of**

(i) money she earns to the money she saves.

(ii) money that she saves to the money she spends.

**Answer:**

(i) Ratio of money that Reena earns to the money she saves

= 150000/50000

= (150000 ÷ 50000)/(50000 ÷ 50000)

**= 3/1 = 3 : 1**

(ii) Money that she spends

= ₹ 1,50,000 – ₹50,000 = ₹1,00,000

∴ Ratio of money she saves to the money she spends

= 50000/100000

= (50000 ÷ 50000)/(100000 ÷ 50000)

**= 1/2 = 1 : 2**

**Question 8. The monthly expenses of a student have increased from ₹350 to ₹500. Find the ratio of**

(i) increase in expenses and original expenses.

(ii) original expenses to increased expenses.

(iii) increased expenses to increased in expenses.

**Answer:**

Original exp. = ₹350

Increased exp. = ₹500

Increased in exp. = 500 – 350 = ₹150

**(i) Increased in exp : original exp.**

= 150 : 350

= 150/350 = 15/35 = 3/7 = 3 : 7

**(ii) Original exp. : Increased exp.**

350 : 500

= 350/500 = 35/50 v= 7/10 = 7 : 10

**(iii) Increased exp : Increase in exp.**

500 : 150

= 500/150 = 50/15 = 10/3 = 10 : 3

**Ratio and Proportion Exe-8.1**

**ML Aggarwal Class 6 ICSE Maths Solutions**

Page-161

**Question 9. Mr Mahajan and his wife are both school teachers and earn ₹20900 and ₹ 18700 per month respectively. Find the ratio of**

(i) Mr Mahajan’s income to his wife’s income.

(ii) Mrs Mahajan’s income to the total income of both.

**Answer:**

**(i) Ratio in Mr Mahajan’s income and his wife**

= 20900 : 18700

= 20900/18700

= 19/17

= 19 : 17

**(ii) Mrs Mahajan’s income to the total income of both**

Earning of Mrs Mahajan = ₹20900

and his wife = ₹ 18700

Total income = ₹39,600

Mrs Mahajan’s income to the total income of both

18700/39600

= 17/36

= 17 : 36

**Question 10. Out of 30 students in a class, 6 like football, 12 like cricket and remaining like tennis. Find the ratio of**

(a) Number of students liking football to number of students liking tennis.

(b) Number of students liking cricket to total number of students.

**Answer:**

Students who like football in the class =6

Students who like cricket in the class =12

The remaining students who like tennis can be obtained by subtracting students who like football and cricket from the total students.

= 30−6−12

= 30−18

= 12

(a) The ratio of the number of students liking football to the number of students liking tennis = 6/12 = 1/2

The ratio of the number of students liking football to the number of students liking tennis is 1:2.

(b) The ratio of the number of students liking cricket to the total number of students = 12/30 = 2/5

The ratio of the number of students liking cricket to the total number of students is 2:5

**Question 11. Which ratio is greater ?**

(i) 3 : 4 or 2 : 3

(ii) 11 : 21 or 15 : 28

**Answer:**

**Question 12. Divide ₹ 560 between Ramu and Munni in the ratio 3 : 2.**

**Answer:**

Total amount = ₹ 560

Ratio in Ramu and Munni = 3 : 2

Sum of ratios = 3 + 2 = 5

Ramu shares = ₹ (560 x 3)/5 = ₹336

Munni shares = ₹ (560 x 2)/5 = ₹224

**Question 13. Two people invested ₹ 15000 and ₹25000 respectively to start a business. They decided to share the profits in the ratio of their investments. If their profit is ₹ 12000, how much does each get?**

**Answer:**

Total investment = 15000 + 25000 = 40000

Investment of 1 st person = 15000/40000 = 3/8

Investment of 2nd person = 1 – (3/8) = 5/8

Total profit = ₹ 12000

Profit of 1st person = 3/8 × ₹12000 = ₹4500

Profit of 2nd person = ₹12000 – ₹4500 = ₹7500

**Question 14. The ratio of Ankur’s money to Roma’s money is 9 : 11. if Ankur has ₹540, how much money does Roma have?**

**Answer:**

Ratio of Ankur’s two Roma’s money = 9 : 11

Ankur has money = ₹540

Let Roma’s have = x

9 :11 :: 540 : x

(9/11) = (540/x)

x = (540 × 11)/9

**x = ₹ 660**

**Question 15. The ratio of weights of tin and zinc in on alloy is 2 : 5. How much zinc is there in 31.5 g of alloy?**

**Answer:**

Ratio of weight = 2 : 5

Sum of ratio = 2 + 5 = 7

Total weight of alloy =31.5g

Part of zinc = 31.5 × 5/7

= 315/10 = 5/7

= 45/2

= 22.5 g

— : End of ML Aggarwal Ratio and Proportion Exe-8.1 Class 6 ICSE Maths Solutions :–

Return to **–** ML Aggarwal Maths Solutions for ICSE Class -6

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