Samacheer Kalvi Class 6 Maths Solutions Term 1 Chapter 3 Ratio and Proportion Exercise 3.4

Question 1. Fill in the blanks.
(i) If the cost of 3 pens is Rs 18, then the cost of 5 pens is ......
(ii) If Karkuzhali earns Rs 1800 in 15 days, then she earns Rs 3000 in ...... days
Answer:
(i) To find the cost of one pen, we divide the total cost by the number of pens: \( \text{Rs } \frac{18}{3} = \text{Rs } 6 \). Then, to find the cost of 5 pens, we multiply the cost of one pen by 5: \( 5 \times 6 = \text{Rs } 30 \). So, the cost of 5 pens is Rs 30.
(ii) We can set up a proportion: \( \frac{\text{Earnings}_1}{\text{Days}_1} = \frac{\text{Earnings}_2}{\text{Days}_2} \). So, \( \frac{1800}{15} = \frac{3000}{x} \). Cross-multiply to solve for \( x \): \( 1800 \times x = 3000 \times 15 \). This means \( x = \frac{3000 \times 15}{1800} = \frac{45000}{1800} = 25 \) days. Proportions are useful for solving problems where quantities change at a constant rate.
In simple words: (i) One pen costs Rs 6, so five pens cost Rs 30. (ii) If she earns Rs 1800 in 15 days, she earns Rs 3000 in 25 days.

🎯 Exam Tip: For fill-in-the-blanks with multiple parts, ensure you answer each sub-question clearly and show the steps for calculation-based questions to get full marks.

Question 2. Say True or False.
(i) If the weight of 40 books is 8 kg, then the weight of 15 books is 3 kg.
(ii) A car travels 90 km in 3 hours with constant speed. It will travel 140 km in 5 hours at the same speed.
Answer:
(i) This statement is True. First, find the weight of one book: \( \frac{8}{40} = \frac{1}{5} \) kg. Then, multiply this by 15 to find the weight of 15 books: \( \frac{1}{5} \times 15 = 3 \) kg. This shows direct proportion where weight increases with the number of books.
(ii) This statement is False. Calculate the car's speed: \( \frac{90 \text{ km}}{3 \text{ hours}} = 30 \) km/hour. Then, find the distance it would cover in 5 hours at this speed: \( 30 \text{ km/hour} \times 5 \text{ hours} = 150 \) km. Since 150 km is not 140 km, the statement is incorrect.
In simple words: (i) Yes, if 40 books weigh 8 kg, then 15 books will weigh 3 kg because each book weighs the same. (ii) No, the car travels 30 km in one hour, so in 5 hours it would travel 150 km, not 140 km.

🎯 Exam Tip: For True or False questions, always show the calculations that support your answer. This proves your understanding, even if the final True/False is simple.

Question 3. If a person reads 20 pages of a book in 2 hours, how many pages will he read in 8 hours at the same speed?
Answer: First, find out how many pages the person reads in 1 hour. We divide the total pages by the total hours: \( \frac{20 \text{ pages}}{2 \text{ hours}} = 10 \) pages per hour. Since the speed is constant, to find out how many pages are read in 8 hours, we multiply the pages per hour by 8: \( 10 \text{ pages/hour} \times 8 \text{ hours} = 80 \) pages. This is an example of a direct proportion, where more time means more pages read.
In simple words: The person reads 10 pages in one hour. So, in 8 hours, they will read 80 pages.

🎯 Exam Tip: Break down rate problems into finding the unit rate (e.g., pages per hour, km per minute) first. This makes it easier to calculate for different total quantities.

Question 4. Cost of 15 chairs is Rs 7500. Find the number of such chairs that can be purchased for Rs 12,000?
Answer: First, determine the cost of one chair. We divide the total cost by the number of chairs: \( \text{Rs } \frac{7500}{15} = \text{Rs } 500 \) per chair. Next, to find how many chairs can be bought for Rs 12,000, we divide the total budget by the cost of one chair: \( \frac{\text{Rs } 12000}{\text{Rs } 500} = 24 \) chairs. Finding the cost per unit is a key step in many real-world pricing problems.
In simple words: Each chair costs Rs 500. So, with Rs 12,000, you can buy 24 chairs.

🎯 Exam Tip: When dealing with costs and quantities, always start by calculating the cost or quantity for a single unit. This unit rate simplifies further calculations.

Question 5. A car covers a distance of 125 km in 5 kg of LP Gas. How much distance will it cover in 3 kg of LP Gas?
Answer: First, calculate how much distance the car covers using 1 kg of LP gas. We divide the total distance by the total gas used: \( \frac{125 \text{ km}}{5 \text{ kg}} = 25 \) km/kg. Then, to find the distance covered in 3 kg of LP gas, multiply the distance per kg by 3: \( 3 \text{ kg} \times 25 \text{ km/kg} = 75 \) km. This type of problem is a direct proportion, where less gas means less distance.
In simple words: The car travels 25 km for every 1 kg of gas. So, with 3 kg of gas, it will travel 75 km.

🎯 Exam Tip: For problems involving fuel consumption, always calculate the mileage or distance covered per unit of fuel first. This makes scaling up or down easy.

Question 6. Cholan walks 6 km in 1 hour at a constant speed. Find the distance covered by him in 20 minutes at the same speed.
Answer: Since 1 hour is equal to 60 minutes, Cholan walks 6 km in 60 minutes. To find the distance he covers in 1 minute, we convert the distance to meters and divide by 60: \( \frac{6 \text{ km}}{60 \text{ min}} = \frac{6000 \text{ m}}{60 \text{ min}} = 100 \) m per minute. Finally, to find the distance covered in 20 minutes, we multiply 100 m/min by 20 min: \( 20 \times 100 \text{ m} = 2000 \text{ m} \). Since 1000 meters makes 1 kilometer, this is equal to 2 km. Unit conversions are often needed when dealing with different units of time or distance.
In simple words: Cholan walks 6 km in 60 minutes. This means he walks 100 meters in one minute. So, in 20 minutes, he walks 2000 meters, which is 2 km.

🎯 Exam Tip: Always make sure your units are consistent. Convert all measurements to a common unit (e.g., minutes to hours, km to meters) before performing calculations.

Question 7. The number of correct answers given by Kaarmugilan and Kavitha in a quiz competition are in the ratio 10 : 11. If they had scored a total of 84 points in the competition, then how many points did Kavitha get?
Answer: The ratio of correct answers is 10:11. To find the total number of parts in the ratio, we add the individual parts: \( 10 + 11 = 21 \) parts. Since 21 parts equal 84 total points, one part is worth \( \frac{84}{21} = 4 \) points. Kavitha's share in the ratio is 11 parts, so her points are \( 11 \times 4 = 44 \) points. Ratios help us understand how parts relate to a whole.
In simple words: The total ratio parts are 21. Since 21 parts make 84 points, each part is 4 points. Kavitha has 11 parts, so she scored 44 points.

🎯 Exam Tip: When solving ratio problems, first find the sum of the ratio parts. Then, divide the total quantity by this sum to find the value of one part.

Question 8. Karmegam made 54 runs in 9 overs and Asif made 77 runs in 11 overs. Whose run rate is better? (run rate = ratio of runs to overs)
Answer: To compare, we need to find the run rate for each player. For Karmegam, the run rate is \( \frac{54 \text{ runs}}{9 \text{ overs}} = 6 \) runs per over. For Asif, the run rate is \( \frac{77 \text{ runs}}{11 \text{ overs}} = 7 \) runs per over. Comparing the two, Asif's run rate of 7 runs per over is better than Karmegam's 6 runs per over. Comparing unit rates helps determine who performed better in such scenarios.
In simple words: Karmegam scored 6 runs per over. Asif scored 7 runs per over. Asif's run rate is better because he scored more runs for each over.

🎯 Exam Tip: To compare performances or rates, always calculate the 'per unit' value for each item. This makes direct comparison straightforward.

Question 9. You purchase 6 apples for Rs 90 and your friend purchases 5 apples for Rs 70. Whose purchase is better?
Answer: To find out whose purchase is better, we need to compare the cost per apple. For your purchase, the cost of 1 apple is \( \frac{\text{Rs } 90}{6} = \text{Rs } 15 \). For your friend's purchase, the cost of 1 apple is \( \frac{\text{Rs } 70}{5} = \text{Rs } 14 \). Since Rs 14 per apple is less than Rs 15 per apple, your friend's purchase is better. Comparing prices on a 'per item' basis helps you get the best deal.
In simple words: Your apples cost Rs 15 each. Your friend's apples cost Rs 14 each. So, your friend got a better deal.

🎯 Exam Tip: To decide which deal is better, always calculate the price of a single item (unit price) for each option and then compare them.

Objective Type Questions

Question 10. If a Barbie doll costs Rs 90, then the cost of 3 such dolls is Rs ___
(a) 260
(b) 270
(c) 30
(d) 93
Answer: (b) 270
In simple words: If one doll costs Rs 90, then three dolls will cost three times that amount. So, Rs 90 multiplied by 3 gives Rs 270.

🎯 Exam Tip: For direct proportion questions like this, simply multiply the unit cost by the desired quantity to find the total cost.

Question 11. If 8 oranges cost Rs 56, then the cost of 5 oranges is Rs ......
(a) 42
(b) 48
(c) 35
(d) 24
Answer: (c) 35
In simple words: First, find the cost of one orange by dividing Rs 56 by 8, which is Rs 7. Then, multiply Rs 7 by 5 to get the cost of 5 oranges, which is Rs 35.

🎯 Exam Tip: In pricing problems, first determine the unit price (cost per single item) before calculating the cost for a different quantity.

Question 12. If a man walks 2 km in 15 minutes, then he will walk ___ km in 45 minutes.
(a) 10
(b) 8
(c) 6
(d) 4
Answer: (c) 6
In simple words: The man walks 2 km in 15 minutes. Since 45 minutes is three times 15 minutes (\( 45 \div 15 = 3 \)), he will walk three times the distance. So, \( 2 \text{ km} \times 3 = 6 \) km.

🎯 Exam Tip: For speed and distance problems with constant speed, look for how many times the time or distance increases to find the corresponding increase in the other quantity.