3. Are the following statements true? (a) 40 persons: 200 persons \( =₹ 15: ₹ 75 \) (b) 7.5 litres: 15 litres \( =5 \mathrm{~kg}: 10 \mathrm{~kg} \) (c) \( 99 \mathrm{~kg}: 45 \mathrm{~kg}=₹ 44: ₹ 20 \) (d) \( 32 \mathrm{~m}: 64 \mathrm{~m}=6 \mathrm{sec}: 12 \mathrm{sec} \) (e) \( 45 \mathrm{~km}: 60 \mathrm{~km}=12 \) hours: 15 hours 4. Determine if the following ratios form a proportion. Also, write the mi and extreme terms where the ratios form a proportion.

Let's evaluate each statement to determine whether the ratios form a true proportion. A proportion is true if the two ratios are equal when simplified. ### 3. Are the following statements true? #### (a) \(40 \text{ persons} : 200 \text{ persons} = ₹15 : ₹75\) - **Simplify both ratios:** - \( \frac{40}{200} = 0.2 \) - \( \frac{15}{75} = 0.2 \) - **Conclusion:** Both ratios are equal. **Answer:** **True** --- #### (b) \(7.5 \text{ litres} : 15 \text{ litres} = 5 \text{ kg} : 10 \text{ kg}\) - **Simplify both ratios:** - \( \frac{7.5}{15} = 0.5 \) - \( \frac{5}{10} = 0.5 \) - **Conclusion:** Both ratios are equal. **Answer:** **True** --- #### (c) \(99 \text{ kg} : 45 \text{ kg} = ₹44 : ₹20\) - **Simplify both ratios:** - \( \frac{99}{45} = 2.2 \) - \( \frac{44}{20} = 2.2 \) - **Conclusion:** Both ratios are equal. **Answer:** **True** --- #### (d) \(32 \text{ m} : 64 \text{ m} = 6 \text{ sec} : 12 \text{ sec}\) - **Simplify both ratios:** - \( \frac{32}{64} = 0.5 \) - \( \frac{6}{12} = 0.5 \) - **Conclusion:** Both ratios are equal. **Answer:** **True** --- #### (e) \(45 \text{ km} : 60 \text{ km} = 12 \text{ hours} : 15 \text{ hours}\) - **Simplify both ratios:** - \( \frac{45}{60} = 0.75 \) - \( \frac{12}{15} = 0.8 \) - **Conclusion:** The ratios are **not** equal. **Answer:** **False** --- ### Summary of Answers: - **(a)** True - **(b)** True - **(c)** True - **(d)** True - **(e)** False --- ### 4. Determine if the following ratios form a proportion. Also, write the mean and extreme terms where the ratios form a proportion. *Since specific ratios were not provided for question 4, here's a general guideline on how to determine proportions and identify mean and extreme terms:* - **Proportion:** Two ratios \( \frac{a}{b} = \frac{c}{d} \) form a proportion if \( a \times d = b \times c \). - **Extreme Terms:** The first and last terms in a proportion, i.e., \(a\) and \(d\). - **Mean Terms:** The middle two terms in a proportion, i.e., \(b\) and \(c\). **Example:** Given the proportion \( \frac{2}{3} = \frac{4}{6} \): - **Extreme Terms:** 2 and 6 - **Mean Terms:** 3 and 4 --- Feel free to provide the specific ratios for question 4 if you need a detailed analysis!