CAT 2022 Question Paper | Quant Slot 3

CAT Previous Year Paper | CAT Quant Questions | Question 10

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 10 : Two cars travel from different locations at constant speeds. To meet each other after starting at the same time, they take 1.5 hours if they travel towards each other, but 10.5 hours if they travel in the same direction. If the speed of the slower car is 60 km/hr, then the distance traveled, in km, by the slower car when it meets the other car while traveling towards each other, is

  1. 150
  2. 100
  3. 90
  4. 120

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Explanatory Answer

Let the distance between the 2 cars be D km.
Let the speeds of the two cars be ‘a’ and ‘b’ respectively and a > b.
Case I)
Cars are moving in the opposite direction (towards each other)
Relative speed = a + b
Time taken = 1.5 hrs
Case II)
Cars are moving in the same direction (Car A chasing Car B)
Relative speed = a - b
Time taken = 10.5 hrs
In both the cases the distance between the cars is the same, ‘D’.
But the time taken is in the ratio 1.5 : 10.5 or 1 : 7
Therefore, the speeds will be in the ratio 7 : 1
a + b = 7(a - b)
8b = 6a
3a = 4b
Substituting b = 60 kmph,
We get, a = 80 kmph.
D = (a + b) * 1.5 = 210km
When they move towards each other the distance covered by them is in the ratio 4 : 3 and the total distance covered by them together is 210 km.
The slower car, B, covers 3/7 th of this 210 km which is 90 km.

The answer is '90'

Choice C is the correct answer.

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