### CAT 2003 Question Paper (Leaked) Question 100

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 100

# Amit wants to reach E2 from N1 using first the chord N1 - W2 and then the inner ring road. What will be his travel time in minutes on the basis of information given in the above question?

Solution

Let the radii of 2 circles be R and r respectively such that R=2*r. Triangle O$$N_2$$$$E_1$$and all the other 3 similar triangles form a right angle at the centre . So using pythagoras theorem the value of chords come out to be $$\sqrt5$$ * R/2 . Hence the total distance traveled is $$\sqrt5$$ * R/2 + 0.5*R*pi. Total time required can be calculated by distance / speed which comes out to be 3.5*R. Among options only 105 is integral multiple of 3.5. 