# CAT 2022 Question Paper | Quant Slot 2

###### CAT Previous Year Paper | CAT Quant Questions | Question 22

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 22 : Two ships meet mid-ocean, and then, one ship goes south and the other ship goes west, both travelling at constant speeds. Two hours later, they are 60 km apart. If the speed of one of the ships is 6 km per hour more than the other one, then the speed, in km per hour, of the slower ship is

1. 12
2. 18
3. 20
4. 24

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Let the speeds of the boats be x kmph and x + 6 kmph.
After 2 hours, the distance travelled by the boats is 2x km and 2x + 12 kms respectively.
The distance between them is 60 kms.
602 = (2x)2 + (2x + 12)2
3600 = 4 x2 + 4 x2 + 144 + 48x
900 = 2 x2 + 36 + 12 x
450 = x2 + 18 + 6 x
x2 + 6x - 432 = 0
x2 + 24x - 18x - 432 = 0
x = 18 or x = -24
The speed of the slower boat is 18 kmph.

Choice B is the correct answer.

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