Write True (T) or False (F) against each of the following statements :
`21 : 6 :: 35 : 10 `

Answer

To determine whether the statement `21 : 6 :: 35 : 10` is true or false, we need to check if the two ratios are equivalent. We will do this by comparing the fractions formed by these ratios.

### Step 1: Write the ratios as fractions
The statement `21 : 6` can be written as the fraction \( \frac{21}{6} \) and `35 : 10` can be written as \( \frac{35}{10} \).

### Step 2: Simplify both fractions
Now, we will simplify both fractions to see if they are equal.

- For \( \frac{21}{6} \):
- The greatest common divisor (GCD) of 21 and 6 is 3.
- So, \( \frac{21 \div 3}{6 \div 3} = \frac{7}{2} \).

- For \( \frac{35}{10} \):
- The GCD of 35 and 10 is 5.
- So, \( \frac{35 \div 5}{10 \div 5} = \frac{7}{2} \).

### Step 3: Compare the simplified fractions
Now we have:
- \( \frac{21}{6} = \frac{7}{2} \)
- \( \frac{35}{10} = \frac{7}{2} \)

Since both fractions are equal, we can conclude that the statement is true.

### Conclusion
The statement `21 : 6 :: 35 : 10` is **True (T)**.

---