CAT 2003 | Question: 1-111

Question

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.

The ratio of the sum of the length of all chord roads, to the length of the outer ring road is

• A. $\sqrt{5} : 2$
• B. $\sqrt{5} : -2$
• C. $\sqrt{5} : \pi$
• D. None of these

Answer 1

Ans: C

length of OR = 2l (let) => length of IR = l

radius of OR = 2r (let) => radius of IR = r (radius is proportional to circumference)

=> length of chord = (r^2 + (2r)^2)^(1/2) = r(5^(1/2))

=> sum of length of all chords / length of OR = 4r(5^(1/2))/4(pi)r = sqrt(5) / (pi)