# CAT 2023 Question Paper | Quant Slot 3

###### CAT Previous Year Paper | CAT Quant Questions | Question 13

CAT 2023 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 13 : A boat takes 2 hours to travel downstream a river from port A to port B, and 3 hours to return to port A. Another boat takes a total of 6 hours to travel from port B to port A and return to port B. If the speeds of the boats and the river are constant, then the time, in hours, taken by the slower boat to travel from port A to port B is

1. $3(3-$sqrt{5})$ 2. $12$$sqrt{5}-2)$ 3. $3$3+$sqrt{5})$ 4. $3$$sqrt{5}-1)$ ## Best CAT Online Coaching Try upto 40 hours for free Learn from the best! #### 2IIM : Best Online CAT Coaching. ### Video Explanation ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now! ### Explanatory Answer Let B1, B2, S be the speeds of the faster boat in still water, speed of slower boat in still water and the speed of the river, and D be the distance between A and B. The first boat takes$2 + 3 = 5) hours for the roundtrip while the second boat takes 6 hours for the roundtrip. This means that the first boat is the faster one.
Since the downstream and upstream times are in the ratio 2 : 3, the downstream and upstream speeds will be in the ratio 3 : 2
$$frac { B _ { 1 } + S } { B _ { 1 } - S } = $frac { 3 } { 2 }$ $2 \left$ B _ { 1 } + S $right$ = 3 $left$ B _ { 1 } - S $right$$ $B _ { 1 } = 5 $times S$ $D = \left$ B _ { 1 } + S $right$ $times 2 = 6 S \times 2 = 12 S$ The second boat takes a total of 6 hours to complete the roundtrip. $\frac { D } { B _ { 2 } + S } + \frac { D } { B _ { 2 } - S } = 6$ $\frac { 2 B _ { 2 } } { B _ { 2 } ^ { 2 } - S ^ { 2 } } = \frac { 6 } { D }$ $\frac { B _ { 2 } } { B _ { 2 } ^ { 2 } - S ^ { 2 } } = \frac { 1 } { 4 S }$ $B _ { 2 } ^ { 2 } - S ^ { 2 } = 4 B _ { 2 } S$ $\div b y S ^ { 2 }$ $\left$ $frac { B _ { 2 } } { S } \right$ ^ { 2 } - 1 = 4 $left$ $frac { B _ { 2 } } { S } \right$$ let $$left$ $frac { B _ { 2 } } { S } \right$ = x$ $x ^ { 2 } - 4 x - 1 = 0$ $x = $frac { 4 \pm \sqrt { 16 + 4 } } { 2 } = 2 \pm \sqrt { 5 }$ $x$ is $+ v e$ $\therefore x = 2 + \sqrt { 5 }$ $B _ { 2 } = S$ 2 + $sqrt { 5 }$$ The time taken by the slower boat to travel from A to B$downstream) = $$frac { D } { B _ { 2 } + S } = $frac { 12 S } {$ 3 + $sqrt { 5 }$ S }$ $= $frac { 12$ 3 - $sqrt { 5 }$ } {$ 3 + $sqrt { 5 } )$ 3 - $sqrt { 5 } ) } = $frac { 12 } { 4 }$ 3 - $sqrt { 5 }$ = 3$ 3 - $sqrt { 5 } )$ The question is " A boat takes 2 hours to travel downstream a river from port A to port B, and 3 hours to return to port A. Another boat takes a total of 6 hours to travel from port B to port A and return to port B. If the speeds of the boats and the river are constant, then the time, in hours, taken by the slower boat to travel from port A to port B is " ##### The answer is '$3$3-$sqrt{5})$' Choice A is the correct answer. ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Prepare for CAT 2024 with 2IIM's Daily Preparation Schedule ###### Know all about CAT Exam Syllabus and what to expect in CAT ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2024 Classroom Batches Starting Now! @Gopalapuram and @Anna nagar ###### Best CAT Coaching in Chennai Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ## CAT Questions | CAT Quantitative Aptitude ## CAT Questions | Verbal Ability for CAT ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Mobile:$91) 99626 48484 / 94459 38484
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