If $70\%$ of a number is $0.35$, then find $120\%$ of that number.

Let the unknown number be $x$.
According to the problem:

$$70\%\text{ of }x=0.35$$

$$\frac{70}{100}\times x=0.35$$

$$0.7\times x=0.35$$

$$x=\frac{0.35}{0.7}=0.5$$

Now, we need to find $120\%$ of this number:

$$\text{Required Value}=120\%\text{ of }x$$

$$\text{Required Value}=\frac{120}{100}\times 0.5=1.2\times 0.5=0.6$$