Question

Two resistors R1 and R2, where R1 > R2, are connected to a voltage source with voltage V. When the resistors are connected in series, the current is Is. When the resistors are connected in parallel, the current from the source is Ip = 10.8Is. What is the ratio R2/R1?

Answer 1

The ratio of the two configurations (series vs parallel) will also have the same ratio. Note this refers to the configuration not to the resistors themselves. There many values of resistors that could provide that, but the problem is not concerned with the specific value of the resistors, just their ratio.

Answer 2

Let R1 be x and R2 be y so x>y. The series configuration would be equal to x + y and Is would be V/(x+y)
The parallel configuration would be equal to: xy/(x+y), the ratio of these configurations is 10.8 So we can establish that x + y = 10.8(xy/(x+y))
Now since you are looking for a ratio, you can arbitrarily assign a value to one of the resistors, say like assign 100 Ohms to x (R1)Solve for y or R2. Then after get R1 and R2 you can solve the ratio of R1 to R2.