Exercise 3.3

Chapter 3: Ratio and Proportion

Class 6 — Solutions Key

Exercise 3.3 — Practice Problems

1. Fill in the boxes.

(i) 3 : 5 :: 12 : 20

Explanation: The terms are in proportion. Since $5 \times 4 = 20$, we multiply the first term by 4: $3 \times 4 = 12$.

(ii) 9 : 24 :: 3 : 8

Explanation: Since $8 \times 3 = 24$, we multiply the third term by 3: $3 \times 3 = 9$.

(iii) 5 : 4 :: 10 : 8 :: 15 : 12

Explanation: The core simplified ratio is $5:4$ (derived from dividing $10:8$ by 2). Multiplying $5:4$ by 3 gives $15:12$.

(iv) 12 : 24 = 2 : 4 = 8 : 16

Explanation: The ratio $8:16$ simplifies to $1:2$. Applying this ratio, $2:4$ and $12:24$ are the equivalent values.

2. Say True or False.

(i) 7 Persons is to 49 Persons as 11 kg is to 88 kg

Answer: False

Reasoning: Ratio 1 is $7 : 49 = 1 : 7$. Ratio 2 is $11 : 88 = 1 : 8$. Since $1 : 7 \neq 1 : 8$, they are not in proportion.

(ii) 10 books is to 15 books as 3 books is to 15 books

Answer: False

Reasoning: Ratio 1 is $10 : 15 = 2 : 3$. Ratio 2 is $3 : 15 = 1 : 5$. Since $2 : 3 \neq 1 : 5$, they are not in proportion.

(iii) If the weight of 40 books is 8 kg, then the weight of 15 books is 3 kg.

Answer: True

Reasoning: Ratio of books to weight is $40 : 8 = 5 : 1$ (5 books weigh 1 kg). For 15 books: $15 \div 5 = 3$ kg.

(iv) A car travels 90 km in 3 hours with constant speed. It will travel 140 km in 5 hours at the same speed.

Answer: False

Reasoning: Speed = $90 \text{ km} \div 3 \text{ hours} = 30 \text{ km/hr}$. In 5 hours, it will travel $30 \text{ km/hr} \times 5 \text{ hours} = 150 \text{ km}$ (not 140 km).

3. Fill in the blanks.

(i) If the cost of 3 pens is ₹18, then the cost of 5 pens is ₹30.

Explanation: Cost of 1 pen = $18 \div 3 = ₹6$. Cost of 5 pens = $5 \times 6 = ₹30$.

(ii) If Karkuzhali earns ₹1800 in 15 days, then she earns ₹3000 in 25 days.

Explanation: Earnings per day = $1800 \div 15 = ₹120$. Number of days to earn ₹3000 = $3000 \div 120 = 25$ days.

4. Find whether 12, 24, 18, 36 are in order that can be expressed as two ratios that are in proportion.

Let the two ratios formed by the terms in order be $12 : 24$ and $18 : 36$.

• First ratio: $12 : 24 = \frac{12}{24} = \frac{1}{2} = \mathbf{1 : 2}$
• Second ratio: $18 : 36 = \frac{18}{36} = \frac{1}{2} = \mathbf{1 : 2}$

Since both ratios are equal ($1 : 2 = 1 : 2$), they are in proportion.

Answer: Yes, 12, 24, 18, and 36 are in proportion (12 : 24 :: 18 : 36).

5. Write the mean and extreme terms in the following ratios and check whether they are in proportion.

(i) 78 litre is to 130 litre and 12 bottles is to 20 bottles

Let the ratio order be $78 : 130 :: 12 : 20$.

• Extreme terms: $78$ and $20$
• Mean terms: $130$ and $12$
• Product of Extremes = $78 \times 20 = \mathbf{1560}$
• Product of Means = $130 \times 12 = \mathbf{1560}$

Since Product of Extremes = Product of Means, they are in proportion.

Answer: They are in proportion.

(ii) 400 gm is to 50 gm and 25 rupees is to 625 rupees

Let the ratio order be $400 : 50 :: 25 : 625$.

• Extreme terms: $400$ and $625$
• Mean terms: $50$ and $25$
• Product of Extremes = $400 \times 625 = \mathbf{250,000}$
• Product of Means = $50 \times 25 = \mathbf{1250}$

Since Product of Extremes $\neq$ Product of Means, they are not in proportion.

Answer: They are NOT in proportion.

6. The America’s famous Golden Gate bridge is 6480 ft long with 756 ft tall towers. A model of this bridge exhibited in a fair is 60 ft long with 7 ft tall towers. Is the model in proportion to the original bridge?

• Original bridge ratio (Length : Tower height) = $6480 : 756$
• Model bridge ratio (Length : Tower height) = $60 : 7$
• Check if they are equal using cross-multiplication (or simplifying):
  Product of Extremes = $6480 \times 7 = \mathbf{45,360}$
  Product of Means = $756 \times 60 = \mathbf{45,360}$

Since Product of Extremes = Product of Means, the dimensions are in proportion.

Answer: Yes, the model is in proportion to the original bridge.

7. 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?

• Pages read in 2 hours = $20$ pages
• Pages read in 1 hour = $20 \div 2 = 10$ pages
• Pages read in 8 hours = $10 \text{ pages/hour} \times 8 \text{ hours} = \mathbf{80 \text{ pages}}$

Answer: 80 pages

8. Cholan walks 6 km in 1 hour at constant speed. Find the distance covered by him in 20 minutes at the same speed.

• Distance in 1 hour (60 minutes) = $6$ km
• Distance in 1 minute = $\frac{6}{60} = \frac{1}{10}$ km
• Distance in 20 minutes = $20 \times \frac{1}{10} = \mathbf{2 \text{ km}}$

Answer: 2 km

9. 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?

• Ratio = $10 : 11$ (Kaarmugilan : Kavitha)
• Total parts = $10 + 11 = 21$ parts
• Total points = $84$
• Value of 1 part = $84 \div 21 = 4$ points
• Kavitha's points = $11 \text{ parts} \times 4 = \mathbf{44 \text{ points}}$

Answer: 44 points

10. Karmegan 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)

• Karmegan's run rate = $\frac{54 \text{ runs}}{9 \text{ overs}} = \mathbf{6 \text{ runs per over}}$
• Asif's run rate = $\frac{77 \text{ runs}}{11 \text{ overs}} = \mathbf{7 \text{ runs per over}}$
• Comparing run rates: $7 > 6$, so Asif has a better run rate.

Answer: Asif's run rate is better.

11. You purchase 6 apples for ₹90 and your friend purchases 5 apples for ₹70. Whose purchase is better?

• Your purchase cost per apple = $90 \div 6 = \mathbf{₹15 \text{ per apple}}$
• Friend's purchase cost per apple = $70 \div 5 = \mathbf{₹14 \text{ per apple}}$
• Comparing prices: ₹14 is cheaper than ₹15, so your friend's purchase is more cost-effective.

Answer: Friend's purchase is better.