Write True (T) or False (F) against each of the following statements :
`16 : 24 :: 20 : 30 `

Answer

To determine whether the statement `16 : 24 :: 20 : 30` is true or false, we need to check if the two ratios are equivalent. Here’s how we can do that step by step:

### Step 1: Write the Ratios as Fractions
We start by converting the ratios into fractions:
- The first ratio, `16 : 24`, can be written as \( \frac{16}{24} \).
- The second ratio, `20 : 30`, can be written as \( \frac{20}{30} \).

### Step 2: Simplify the Fractions
Next, we simplify both fractions:
- For \( \frac{16}{24} \):
- Both the numerator and denominator can be divided by their greatest common divisor (GCD), which is 8.
- So, \( \frac{16 \div 8}{24 \div 8} = \frac{2}{3} \).

- For \( \frac{20}{30} \):
- Both the numerator and denominator can be divided by their GCD, which is 10.
- So, \( \frac{20 \div 10}{30 \div 10} = \frac{2}{3} \).

### Step 3: Compare the Simplified Fractions
Now, we compare the simplified fractions:
- We have \( \frac{16}{24} = \frac{2}{3} \) and \( \frac{20}{30} = \frac{2}{3} \).

### Step 4: Conclusion
Since both fractions are equal, we can conclude that the statement `16 : 24 :: 20 : 30` is true.

### Final Answer
True (T)

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