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CAT 2003 Slot 2 — QA Question 36

Height & DistanceEasy
Passage / Data

Answer the following question based on the information given below.

A string of three English letters is formed as per the following rules:

  1. The first letter is any vowel.
  2. The second letter is m, n or p.
  3. If the second letter is m, then the third letter is any vowel which is different from the first letter.
  4. If the second letter is n, then the third letter is e or u.
    1. If the second letter is p, then the third letter is the same as the first letter.

A car is being driven, in a straight line and at a uniform speed, towards the base of a vertical tower. The top of the tower is observed from the car and, in the process, it takes 10 minutes for the angle of elevation to change from 45° to 60°. After how much more time will this car reach the base of the tower?

Answer & solution

  • 5(3+1)

  • B

    6(3+1)

  • C

    7(3-1)

  • D

    8(3-2)

Solution

Let x be the distance from the later position of the car and the tower (i.e. when the angle of elevation was 60°).

Since the triangle formed (i.e. ∆ABD) is a 30°-60°-90° triangle, we have,

height of the tower, h = x3

Now, since the triangle formed by the initial position of the car (i.e. ∆ABC) is an isosceles triangle, AB = BC

i.e. BC = x3

∴ DC = x3 - x = x(3 - 1)

Time taken to travel distance DC is 10 minutes, thus,

Speed s=x(3-1)10

Time taken to travel distance x = xx(3-1)10=103-1=5(3+1)

Hence, option (a).

CAT 2003 Slot 2 QA Q36: A car is being driven, in a straight line and at a uniform speed, towards the base of a vertical tower. The to — Solution | TheCATExam