Write True (T) or False (F) against each of the following statements :
`8:9 :: 24 : 27 `

Answer

To determine whether the statement \( 8:9 :: 24:27 \) is true or false, we need to check if the two ratios are equivalent. We can do this by comparing the fractions formed by these ratios.

### Step-by-Step Solution:

1. **Write the Ratios as Fractions**:
- The first ratio \( 8:9 \) can be written as the fraction \( \frac{8}{9} \).
- The second ratio \( 24:27 \) can be written as the fraction \( \frac{24}{27} \).

2. **Simplify the Second Fraction**:
- To simplify \( \frac{24}{27} \), we can divide both the numerator and the denominator by their greatest common divisor (GCD).
- The GCD of 24 and 27 is 3.
- So, \( \frac{24 \div 3}{27 \div 3} = \frac{8}{9} \).

3. **Compare the Two Fractions**:
- Now we have \( \frac{8}{9} \) from the first ratio and \( \frac{8}{9} \) from the simplified second ratio.
- Since both fractions are equal, we can conclude that the two ratios are equivalent.

4. **Conclusion**:
- Since \( \frac{8}{9} = \frac{24}{27} \), we can say that the statement \( 8:9 :: 24:27 \) is **True (T)**.

### Final Answer:
- The statement \( 8:9 :: 24:27 \) is **True (T)**.