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.

Question

UpStudy AI · Accepted Answer

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) $$40 	ext{ persons} : 200 	ext{ persons} = ₹15 : ₹75$$

- **Simplify both ratios:**
  - $$ \frac{40}{200} = 0.2 $$
  - $$ \frac{15}{75} = 0.2 $$

- **Conclusion:** Both ratios are equal.
  
**Answer:** **True**

---

#### (b) $$7.5 	ext{ litres} : 15 	ext{ litres} = 5 	ext{ kg} : 10 	ext{ kg}$$

- **Simplify both ratios:**
  - $$ \frac{7.5}{15} = 0.5 $$
  - $$ \frac{5}{10} = 0.5 $$

- **Conclusion:** Both ratios are equal.
  
**Answer:** **True**

---

#### (c) $$99 	ext{ kg} : 45 	ext{ kg} = ₹44 : ₹20$$

- **Simplify both ratios:**
  - $$ \frac{99}{45} = 2.2 $$
  - $$ \frac{44}{20} = 2.2 $$

- **Conclusion:** Both ratios are equal.
  
**Answer:** **True**

---

#### (d) $$32 	ext{ m} : 64 	ext{ m} = 6 	ext{ sec} : 12 	ext{ sec}$$

- **Simplify both ratios:**
  - $$ \frac{32}{64} = 0.5 $$
  - $$ \frac{6}{12} = 0.5 $$

- **Conclusion:** Both ratios are equal.
  
**Answer:** **True**

---

#### (e) $$45 	ext{ km} : 60 	ext{ km} = 12 	ext{ hours} : 15 	ext{ hours}$$

- **Simplify both ratios:**
  - $$ \frac{45}{60} = 0.75 $$
  - $$ \frac{12}{15} = 0.8 $$

- **Conclusion:** The ratios are **not** equal.
  
**Answer:** **False**

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### Summary of Answers:

- **(a)** True
- **(b)** True
- **(c)** True
- **(d)** True
- **(e)** False

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### 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 $$ a 	imes d = b 	imes c $$.
  
- **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

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Feel free to provide the specific ratios for question 4 if you need a detailed analysis!
**3. Are the following statements true?** - **(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.** - **Proportion:** Two ratios $$ \frac{a}{b} = \frac{c}{d} $$ form a proportion if $$ a 	imes d = b 	imes c $$. - **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

Are the following statements true?
(a) 40 persons: 200 persons $₹ ₹$
(b) 7.5 litres: 15 litres
© $₹ ₹$
(d)
(e) hours: 15 hours

Determine if the following ratios form a proportion. Also, write the mi
and extreme terms where the ratios form a proportion.

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