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CAT 2003 Slot 1 — QA Question 11

2 CirclesEasy
Passage / Data

Answer the following question based on 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 endpoint of IR. Traffic moves at a constant speed of 30π km/hr on the OR road, 20π km/hr on the IR road, and km/hr on all the chord roads.

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

Answer & solution

  • A

    5:2

  • B

    5:2π

  • 5:π

  • D

    None of the above

Solution

Consider the diagram below as per the conditions given in the question,

Speed on outer ring road = 30π km/hr

Speed on inner ring road = 20π km/hr

And speed on chord roads = 155 km/hr

Let R and r be radii of the Outer Ring road and the Inner Ring road respectively.

∵ Outer Ring road is twice as long as Inner Ring road, we have,

∴ 2πR = 2 × (2πr)

∴ R = 2r

∴ Length of inner ring road = 2πr km and outer ring road = 4πr km

In the figure above, in ∆OW2N1,

W2N1 = (2r)2+r2=5r km

∴ Length of the chord road = 5r km

∴ Ratio of the length of all chord roads to length of the outer ring road = 45r4πr=5π

Hence, option (c).

CAT 2003 Slot 1 QA Q11: The ratio of the sum of the lengths of all chord roads to the length of the outer ring road is — Solution | TheCATExam