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Answer the question on the basis of the information given below:

A city has two perfectly circular and concentric ring roads, the outer ring road (OR) being twice as long as the inner ring road (IR). There are also four (straight line) chord roads from $\text{E1},$ the east end point of OR to $\text{N2}$, the north end point of IR; from $\text{N1}$, the north end point of OR to $\text{W2}$, the west end point of IR; from $\text{W1}$, the west end point of OR, to $\text{S2}$, the south end point of IR; and from $\text{S1}$, the south end point of OR to $\text{E2}$, the east end point of IR. Traffic moves at a constant speed $30 \pi \: \text{km/hr}$ on the OR road, $20 \pi \: \text{km/hr}$ on the IR road, and $15 \sqrt{5} \: \text{km/hr}$ on all chord roads.

Amit wants to reach $\text{N2}$ from $\text{S1}.$ It would take him $90$ minutes if he goes on minor arc $\text{S1 - E1}$ on OR, and then on the chord road $\text{E1 - N2}.$ What is the radius of the outer ring road in km?

  1. $60$
  2. $40$
  3. $30$
  4. $20$
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