Write 'T' for true and 'F' for false for the statement given below:
a. 30, 40, 45, 60 are in proportion.
b. 6:8 and 9: 12 are equivalent ratios of 3 : 4.
c. a dozen : a score = 5:3.
d. 60 p : ₹ 3 = 1:5.

Answer

To determine whether each statement is true (T) or false (F), we will analyze each statement step by step.

### Step 1: Analyze the first statement
**Statement a:** 30, 40, 45, 60 are in proportion.

1. To check if these numbers are in proportion, we need to compare the ratios:
\[ \frac{30}{40} \quad \text{and} \quad \frac{45}{60} \]
2. Simplifying both fractions:
- For \(\frac{30}{40}\):
\[ \frac{30 \div 10}{40 \div 10} = \frac{3}{4} \]
- For \(\frac{45}{60}\):
\[ \frac{45 \div 15}{60 \div 15} = \frac{3}{4} \]
3. Since both fractions are equal (\(\frac{3}{4} = \frac{3}{4}\)), the statement is **True (T)**.

### Step 2: Analyze the second statement
**Statement b:** 6:8 and 9:12 are equivalent ratios of 3:4.

1. We will convert both ratios into fractions:
\[ \frac{6}{8} \quad \text{and} \quad \frac{9}{12} \]
2. Simplifying both fractions:
- For \(\frac{6}{8}\):
\[ \frac{6 \div 2}{8 \div 2} = \frac{3}{4} \]
- For \(\frac{9}{12}\):
\[ \frac{9 \div 3}{12 \div 3} = \frac{3}{4} \]
3. Both ratios simplify to \(\frac{3}{4}\), which confirms they are equivalent to 3:4. Therefore, the statement is **True (T)**.

### Step 3: Analyze the third statement
**Statement c:** A dozen : a score = 5:3.

1. A dozen equals 12 and a score equals 20, so we write:
\[ 12:20 \]
2. Converting this into a fraction:
\[ \frac{12}{20} \]
3. Simplifying:
\[ \frac{12 \div 4}{20 \div 4} = \frac{3}{5} \]
4. The ratio we found is 3:5, which is not equal to 5:3. Therefore, the statement is **False (F)**.

### Step 4: Analyze the fourth statement
**Statement d:** 60 p : ₹ 3 = 1:5.

1. First, convert ₹ 3 into paise. Since 1 rupee = 100 paise:
\[ ₹ 3 = 3 \times 100 = 300 \text{ paise} \]
2. Now we have the ratio:
\[ 60 \text{ paise} : 300 \text{ paise} \]
3. Converting this into a fraction:
\[ \frac{60}{300} \]
4. Simplifying:
\[ \frac{60 \div 60}{300 \div 60} = \frac{1}{5} \]
5. The ratio simplifies to 1:5, which matches the statement. Therefore, the statement is **True (T)**.

### Final Answers
- a. T
- b. T
- c. F
- d. T