Step 1: Understand the concept of flow index.
The flow index is a measure of the plasticity of soil and is calculated using the formula: $$ \text{Flow Index} = \text{Moisture Content at 10 Blows} - \text{Moisture Content at 100 Blows} $$ Given:
Moisture content at 10 blows = $ 70% $
Moisture content at 100 blows = $ 20% $
Step 2: Apply the formula. $$ \text{Flow Index} = 70% - 20% = 50% $$
Step 3: Evaluate other options.
$ 20% $: Incorrect; this is only the final moisture content.
$ 35% $: Incorrect; not derived from any standard calculation.
$ 70% $: Incorrect; this is the initial moisture content.
Step 4: Select the correct option.
Based on the calculation, the correct value is: $$ \boxed{50%} $$