1. Given ratio:  \frac{12 \text{ problems}}{42 \text{ minutes}} 
2. Let \( x \) be the number of minutes to solve 20 problems:  \frac{20 \text{ problems}}{x \text{ minutes}} 
3. Equate the ratios:  \frac{12}{42} = \frac{20}{x} 
4. Cross-multiply:  12x = 42 \times 20 
5. Solve for \( x \):  12x = 840 
6.  x = \frac{840}{12} 
7.  x = 70 
Therefore, it will take \( x = 70 \text{ minutes} \).