CAT 2022 Question Paper | Quant Slot 3

CAT Previous Year Paper | CAT Quant Questions | Question 21

CAT 2022 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 21 : Two ships are approaching a port along straight routes at constant speeds. Initially, the two ships and the port formed an equilateral triangle with sides of length 24 km. When the slower ship travelled 8 km, the triangle formed by the new positions of the two ships and the port became right-angled. When the faster ship reaches the port, the distance, in km, between the other ship and the port will be

  1. 8
  2. 12
  3. 6
  4. 4

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Explanatory Answer

Let us denote the port by P,
the slower ship by S.
the faster ship by F.
Ships and Port
Let their new positions be A and B.
Ships and Port
Triangle APB is right-angled, We know that angle APB is 60 degrees, because triangle SFA is equilateral. The right angle must be at point B, because angle PAB is less than 60 degrees.
sin(30) = \( \frac { 1 } { 2 } = \frac { B P } { A P } \)
BP = 0.5(AP) = 8
BF = FP - BP = 24 - 8 = 16
That mean, the faster ship is twice as fast as the slower one.
So, when the faster ship reaches the Port covering 24 km, the slower ship covers only 12 km and has remaining 12 km left to cover.

The answer is '12'

Choice B is the correct answer.

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