### CAT 2003 Question Paper (Leaked) Question 99

Instructions

DIRECTIONS for the following three questions: Answer the questions 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 E1, the east end point of OR to N2, the north end point of IR; from N1, the north end point of OR to W2, the west end point of IR; from W1, the west end point of OR, to S2, the south end point of IR; and from S1 the south end point of OR to E2, the east end point of IR. Traffic moves at a constant speed of $$30\pi$$ km/hr on the OR road, 20$$\pi$$ km/hr on the IR road, and 15$$\sqrt5$$ km/hr on all the chord roads.

Question 99

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

Solution

We know that the total time taken is 1.5 hrs. Calculating the individual time taken and the adding and then equating to 1.5.

$$\frac{\pi*R}{2*30*\pi} + \frac{\sqrt{5}*R}{2*15*\sqrt{5}}$$ = 1.5 solving we get R=30. 