Samacheer Kalvi Class 6 Maths Solutions Term 1 Chapter 3 Ratio and Proportion Exercise 3.1

Question 1. Fill in the blanks.
(i) Ratio of Rs 3 to Rs 5 = ____
(ii) Ratio of 3 m to 200 cm = ____
(iii) Ratio of 5 km 400 m to 6 km = ____
(iv) Ratio of 75 paise to Rs 2 = ____
Answer:
(i) To find the ratio of Rs 3 to Rs 5, we write them as \( 3 : 5 \). Since both amounts are already in rupees, we can directly form the ratio. This ratio is already in its simplest form.
(ii) For the ratio of 3 m to 200 cm, we first change meters to centimeters. Since 1 meter is 100 centimeters, 3 meters will be \( 3 \times 100 = 300 \) cm. So the ratio is 300 cm : 200 cm, which simplifies to \( 3 : 2 \).
(iii) To find the ratio of 5 km 400 m to 6 km, we convert everything to meters. 5 km 400 m is \( 5 \times 1000 + 400 = 5400 \) m. 6 km is \( 6 \times 1000 = 6000 \) m. The ratio is \( 5400 : 6000 \), which simplifies to \( 9 : 10 \).
(iv) For the ratio of 75 paise to Rs 2, we change rupees to paise. Since Rs 1 is 100 paise, Rs 2 will be \( 2 \times 100 = 200 \) paise. The ratio is 75 paise : 200 paise, which simplifies to \( 3 : 8 \). Ratios compare quantities, so they must always be in the same unit.
In simple words: When finding ratios, make sure both parts are in the same unit (like rupees or centimeters) before simplifying. Divide both numbers by their largest common factor to get the simplest ratio.

🎯 Exam Tip: Always convert quantities to the same unit before calculating a ratio. For example, convert kilometers to meters or rupees to paise.

Question 2. Say whether the following statements are True or False.
(i) The ratio of 130 cm to 1 m is 13 : 10
(ii) One of the terms in a ratio cannot be 1
Answer:
(i) This statement is True. We know that 1 meter is equal to 100 centimeters. So, the ratio of 130 cm to 1 m becomes the ratio of 130 cm to 100 cm. When we simplify \( 130 : 100 \), by dividing both numbers by 10, we get \( 13 : 10 \).
(ii) This statement is False. A ratio can definitely have 1 as one of its terms. For example, the ratio of 5 apples to 5 oranges is \( 5 : 5 \), which simplifies to \( 1 : 1 \). Similarly, the ratio of 1 book to 2 pens is \( 1 : 2 \). Ratios simply show how quantities relate to each other, and one of them can be 1.
In simple words: Statement (i) is true because 130 cm to 100 cm simplifies to 13:10. Statement (ii) is false because ratios like 1:2 are very common and valid.

🎯 Exam Tip: Remember to convert units when comparing them in a ratio. Also, understand that a ratio can include the number 1.

Question 3. Find the simplified form of the following ratios.
(i) 15:20
(ii) 32 : 24
(iii) 7: 15
(iv) 12:27
(v) 75 : 100
Answer:
(i) \( 15 : 20 \)
To simplify, we find the greatest common factor (GCF) of 15 and 20. The GCF is 5.
Divide both numbers by 5: \( 15 \div 5 = 3 \) and \( 20 \div 5 = 4 \).
So, the simplified ratio is \( 3 : 4 \).
(ii) \( 32 : 24 \)
The greatest common factor of 32 and 24 is 8.
Divide both numbers by 8: \( 32 \div 8 = 4 \) and \( 24 \div 8 = 3 \).
So, the simplified ratio is \( 4 : 3 \).
(iii) \( 7 : 15 \)
The numbers 7 and 15 do not have any common factors other than 1. This means the ratio is already in its simplest form.
So, the simplified ratio is \( 7 : 15 \).
(iv) \( 12 : 27 \)
The greatest common factor of 12 and 27 is 3.
Divide both numbers by 3: \( 12 \div 3 = 4 \) and \( 27 \div 3 = 9 \).
So, the simplified ratio is \( 4 : 9 \).
(v) \( 75 : 100 \)
The greatest common factor of 75 and 100 is 25.
Divide both numbers by 25: \( 75 \div 25 = 3 \) and \( 100 \div 25 = 4 \).
So, the simplified ratio is \( 3 : 4 \). Simplifying ratios helps us compare them easily.
In simple words: To simplify a ratio, divide both numbers by the biggest number that can divide both of them evenly. Keep dividing until you can't anymore, and that's the simplest form.

🎯 Exam Tip: Always look for the greatest common factor (GCF) to simplify ratios in one step, or simplify in multiple steps by dividing by any common factor until no more common factors exist (other than 1).

Question 4. Akilan walks 10 km in an hour while Selvi walks 6 km in an hour. Find the simplest ratio of the distance covered by Akilan to that of Selvi.
Answer: Akilan's distance is 10 km, and Selvi's distance is 6 km. We need to find the ratio of Akilan's distance to Selvi's distance.
Ratio of Akilan's distance to Selvi's distance \( = 10 \text{ km} : 6 \text{ km} \)
To simplify this ratio, we find the greatest common factor of 10 and 6, which is 2.
We divide both numbers by 2:
\( 10 \div 2 = 5 \)
\( 6 \div 2 = 3 \)
So, the simplest ratio of the distance covered by Akilan to that of Selvi is \( 5 : 3 \). This tells us that for every 5 km Akilan walks, Selvi walks 3 km in the same amount of time.
In simple words: Akilan walks 10 km and Selvi walks 6 km. Their ratio is 10:6. When we simplify it by dividing by 2, we get 5:3.

🎯 Exam Tip: When setting up a ratio, make sure the order of the items in the ratio matches the order asked in the question (e.g., Akilan to Selvi). Then simplify to the smallest whole numbers.

Question 5. The cost of parking a bicycle is Rs 5 and the cost of parking a scooter is Rs 15. Find the simplest ratio of the parking cost of a bicycle to that of a scooter.
Answer: The cost of parking a bicycle is Rs 5. The cost of parking a scooter is Rs 15. We need to find the ratio of the bicycle's parking cost to the scooter's parking cost.
Ratio of bicycle parking cost to scooter parking cost \( = \text{Rs } 5 : \text{Rs } 15 \)
To simplify this ratio, we find the greatest common factor of 5 and 15, which is 5.
We divide both numbers by 5:
\( 5 \div 5 = 1 \)
\( 15 \div 5 = 3 \)
So, the simplest ratio of the parking cost of a bicycle to that of a scooter is \( 1 : 3 \). This means parking a scooter costs three times as much as parking a bicycle. Ratios help us compare prices effectively.
In simple words: A bicycle costs Rs 5 to park, and a scooter costs Rs 15. The ratio of their parking costs is 5:15. We divide both numbers by 5 to get the simplest ratio, which is 1:3.

🎯 Exam Tip: Always simplify ratios to their lowest terms. This makes the comparison clearer and easier to understand.

Question 6. Out of 50 students in a class, 30 are boys. Find the ratio of
(i) number of boys to the number of girls.
(ii) the number of girls to the total number of students.
(iii) the number of boys to the total number of students.
Answer:
Total number of students in the class = 50
Number of boys = 30
Number of girls = Total students - Number of boys \( = 50 - 30 = 20 \)

(i) Ratio of number of boys to the number of girls:
\( = \text{Number of boys} : \text{Number of girls} \)
\( = 30 : 20 \)
To simplify, divide both numbers by their GCF, which is 10.
\( = 30 \div 10 : 20 \div 10 \)
\( = 3 : 2 \)

(ii) Ratio of the number of girls to the total number of students:
\( = \text{Number of girls} : \text{Total number of students} \)
\( = 20 : 50 \)
To simplify, divide both numbers by their GCF, which is 10.
\( = 20 \div 10 : 50 \div 10 \)
\( = 2 : 5 \)

(iii) Ratio of the number of boys to the total number of students:
\( = \text{Number of boys} : \text{Total number of students} \)
\( = 30 : 50 \)
To simplify, divide both numbers by their GCF, which is 10.
\( = 30 \div 10 : 50 \div 10 \)
\( = 3 : 5 \)
These ratios help us understand the composition of the class quickly.
In simple words: First, find out how many girls there are. Then, for each part, write the numbers in the correct order and simplify the ratio by dividing by the largest common factor.

🎯 Exam Tip: Always make sure to calculate all necessary quantities (like the number of girls) before forming the ratios. Pay attention to the order specified in each ratio calculation.

Objective Type Questions

Question 7. The ratio of Rs 1 to 20 paise is ____
(a) 1:5
(b) 1:2
(c) 2:1
(d) 5:1
Answer: (d) 5:1
In simple words: Change Rs 1 into 100 paise. Then the ratio is 100 paise to 20 paise, which simplifies to 5:1.

🎯 Exam Tip: When dealing with money, convert everything to the smallest unit (paise in this case) before finding the ratio to avoid mistakes.

Question 8. The ratio of 1 m to 50 cm is
(a) 1:50
(b) 50 : 1
(c) 2:1
(d) 1:2
Answer: (c) 2:1
In simple words: Change 1 meter into 100 centimeters. Then the ratio is 100 cm to 50 cm, which simplifies to 2:1.

🎯 Exam Tip: In length problems, always convert meters to centimeters (or vice versa) so both parts of the ratio are in the same unit.

Question 9. The length and breadth of a window are 1 m and 70 cm respectively. The ratio of the length to the breadth is
(a) 1:7
(b) 7:1
(c) 7: 10
(d) 10:7
Answer: (d) 10:7
In simple words: Convert the length from 1 meter to 100 cm. Then the ratio of length (100 cm) to breadth (70 cm) is 100:70, which simplifies to 10:7.

🎯 Exam Tip: Remember to express both measurements in the same unit (e.g., centimeters) before finding the ratio to ensure correctness.

Question 10. The ratio of the number of sides of a triangle to the number of sides of a rectangle is
(a) 4:3
(b) 3:4
(c) 3:5
(d) 3:2
Answer: (b) 3:4
In simple words: A triangle has 3 sides and a rectangle has 4 sides. So, the ratio of a triangle's sides to a rectangle's sides is 3:4.

🎯 Exam Tip: Recall the basic properties of common geometric shapes, like the number of sides, to answer such questions accurately.

Question 11. If Azhagan is 50 years old and his son is 10 years old then the simplest ratio between the age of Azhagan to his son is
(a) 10:50
(b) 50 : 10
(c) 5:1
(d) 1:5
Answer: (c) 5:1
In simple words: Azhagan is 50 and his son is 10. The ratio of Azhagan's age to his son's age is 50:10. When we simplify this by dividing both numbers by 10, we get 5:1.

🎯 Exam Tip: Always ensure the ratio is in its simplest form. For age ratios, simply divide both ages by their greatest common factor.