BIMTECH PGDM Admissions 2026
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CAT Exam Breakthrough: Problems on Trains, Boat and Stream Questions For CAT Exam - Day 31
The CAT exam for MBA admissions in 2025-2027 will be conducted on November 24, 2024. Here is the plan for day 30 of Careers360's 60-day CAT 2024 preparation guide. This will help you study for the CAT exam.
The major focus of this article is the problem of Trains, Relative Speed aptitude questions, Boat and Stream questions, Decision Making (part 2), and direct and indirect VARC questions. Students will gain knowledge of various sections, comprehend ideas, and experiment with methods for answering both direct and indirect multiple-choice questions.
LiveIIM CAT 2025 Result (OUT) LIVE: MBA admission criteria for IIMs; CAT score weightage, cut-offsDec 26, 2025 | 11:01 PM ISTRead More
IIM Kozhikode will retain its three-stage admission process for the MBA (PGP) 2026–28 batch, with CAT 2025 scores carrying a final weightage of 35 percent. The minimum overall CAT cut-off for general category candidates remains at 85 percentile, with sectional qualifying scores required in VARC, DILR, and QA. Shortlisting of candidates will be based on CAT performance, academic record, and personal interview rounds.
CAT Preparation 2024 in 60 Days
Part-1: Quantitative Aptitude for CAT Exam
Important Concept/Formula Used in Relative Speed aptitude questions and problems on trains
Problems on trains: Trains (Length L1 and L2) Approaching each other with velocities v1 and v2.
Time taken to Cross each other = (L1+L2)/(v1+v2)
Trains (Length L1 and L2) moving in the same direction with velocities v1 and v2. (v1 > v2)
Time taken to overtake = (L1+L2)/(V1-V2)
Concept of upstream:
CAT 2025 College Predictor
Use CAT 2025 College Predictor to check your chances for IIM and top MBA calls based on CAT percentile, profile, work experience and cut-off trends.
Use NowSpeed of boat in upstream = Vu = v – u
v = speed of boat in still water
u = speed of river/flow/current
Concept of downstream
Speed of boat in downstream = Vu = v + u
CAT Exam:
Previous Year CAT Questions On Time, Speed and Distance (CAT questions on Boats and Streams)
Train Aptitude Questions
Q1. Train T leaves station X for station Y at 3 pm. Train S, travelling at three-quarters of the speed of T, leaves Y for X at 4 pm. The two trains pass each other at station Z, where the distance between X and Z is three-fifths of that between X and Y. How many hours does train T take for its journey from X to Y? [TITA: CAT 2018]
Relative Speed Aptitude Questions with Solution:
Let the total distance between X and Y = 5a, therefore the distance between X and Z = 3a & between Y and Z = 2a.
The ratio of time taken by train T and train S to reach Z from their respective Station = (3a/v: 2a/3v/4 = 9: 8) where v is the velocity of train T.
Let time taken by train T is 9y, then the time taken by train S will be 8y.
Therefore, (9y -1) = 8y
⇒ y = 1
so, time taken by train T to cover 3a = 9 hour
so, time taken by train T to cover XY (5a) = 5/3 x 9 = 15 hour
Boats and Streams Aptitude Problems
Q2. A man travels by motor boat down a river to his office and back. With the speed of the river unchanged, if he doubles the speed of his motorboat, then his total travel time gets reduced by 75%. The ratio of the original speed of the motor boat to the speed of the river is [CAT 2017]
6: 2
7: 2
25: 3
3: 2
Boat and Stream Questions With Solution: [B]
Let the speed of the boat in still water and the speed of the river be v and u respectively. D is the width of the river.
So, D/v+u+ D/v-u = Time taken (with original speed of motor boat)
and D/2v+u+ D/2v-u = Time taken (with the double speed of motor boat)
According to the question, travel time is reduced by 75% which means new time is ¼ of old time.
So, 4D/2v+u+ 4D/2v-u= D/v+u+ D/v-u
On solving, we get v: u = 7: 2
CAT entrance exam: Prerequisite for quantitative aptitude for CAT questions:
Ratios, Proportion and variations
Basics of Time, Speed and distance
CAT Exam Important Topic: Strategy to Prepare “Basics of Time, speed and Distance (Trains and Boats)” and problems on trains
a km/hr= (a x 5/18) m/s
Time taken by a train of length L to cross a man or pole is equal to L/v.
Time taken by a train of length L to cross a stationary object of length x is equal to (L + x)/v.
If the two objects start from A and B with speeds u and v respectively, and after crossing each other take a and b hours to reach B and A respectively, then u: v = √b: √a.
Divide questions topic-wise and practice different problems based on CAT Previous years questions.
CAT study material: References to Study (Theory)
How to Prepare for Quantitative Aptitude for CAT by Arun Sharma (7th Edition)
For Problems on Trains: Mission CAT (YouTube, Link: https://www.youtube.com/watch?v=v-383fMptOI)
For Boats and Stream: Rodha (YouTube) Link: https://www.youtube.com/watch?v=vx3DfHuuY6Y
CAT study material: References to Practice Problems on Trains, Boat and Stream Problems
Quantitative Aptitude for the CAT – Sarvesh Verma.
Trains: AlphaNumeric (YouTube) (Link: https://www.youtube.com/watch?v=n0TMtPq5NlQ)
CAT Sample Papers and previous years questions.
Part 2: CAT 2024 Preparation Tips: CAT DILR Tips (Logical Reasoning and Data Interpretation)
CAT 2024 Syllabus Topic: Strategy to prepare “Decision Making” (Part-2)
Sample Questions Based on the CAT/XAT Exam:
Comprehension:
A device classifies numbers according to the following criteria. The number must have
seven digits.
at least two prime digits.
perfect squares as the first and the last digits.
an even digit as the middle digit. If the number satisfies criteria (A), (B), (C) and (D) then the number is classified as a Superior number.
If a number is a superior number and the digits are in increasing order from left to right according to the value, then the number is classified as an impressive number.
If the number satisfies criteria (A), (B) and (D) but not (C), but the first and last digits are even, then the number is classified as a Mutual number.
If the number satisfies criteria (A) (B) and (C) but not (D) but all the digits are odd, then the number is classified as a Classic number.
If the number does not fall under any of the above-mentioned classifications, then the number is classified as a Garbage number. Based on the above criteria, decide which number should be classified in which of the above-mentioned classification.
Mark your answer choice as
(A), if the number is classified as a Superior number.
(B), if the number is classified as an impressive number.
(C), if the number is classified as a Mutual number.
(D), if the number is classified as a Classic number.
(E), if the number is classified as a Garbage number.
Classify the following number as mentioned above.
1778459
4276891
1367574
9632578
4556666
4368579
1366789
9517531
1573934
964374
Solution:
Tip: Summarize the details given in the form of table:
Ans
A
A
E
E
C
A
B
D
E
E
CAT Entrance Exam: Prerequisite
Analytical Skills
Decision Making: Concepts
Tips and Tricks for CAT
Practice XAT Sample Papers.
Practice XAT Previous Years Papers.
Do not waste much time on it if preparing for CAT.
Much important for XAT Exam.
References to CAT Study (Theory)
Verbal and Non- Verbal Reasoning by B S Sijwali
CAT LRDI by Nishit K Sinha
References to Practice
Verbal and Non-Verbal Reasoning by R S Agrawal.
CAT/XAT Previous years Papers and Sample Papers.
Part-3: CAT Exam Preparation 2024: CAT Exam Tips For VARC (Verbal Ability & Reading Comprehension)
CAT Exam Important Topic: Strategy to Prepare “Direct and Indirect Speech” for CAT-2024
CAT Important Concepts
Changes from direct to indirect require
Changes in Tense
Changes in Person and Pronouns
Changes in Time Phrases
CAT Previous Years' MCQs on Direct and Indirect:
Question 1: Direct: He said, “Will you come for the meeting?”
Indirect:
He asked them whether he would come for the meeting.
He asked them that he will come for the meeting.
He said to them whether he will come for the meeting.
None of these
Ans: A
Explanation: Future tense changes to present conditional.
Question 2: Direct: She said, “I have baked a cake.”
Indirect:
She said that she baked a bake.
She said that she had baked a cake.
She said whether she had baked a cake.
None of these.
Ans: B
Explanation: Present perfect changes to past perfect.
CAT 2024:Prerequisite
The basic idea of Tenses.
Knowledge of subject-verb and object.
Tips and Tricks for CAT Exam
Recognize the structure carefully.
All inverted commas or quotation marks are omitted and the sentence ends with a full stop.
Conversion rules:
Simple Present Changes to Simple Past.
Present Continuous Changes to Past Continuous.
Present Perfect Changes to Past Perfect
Simple Past Changes to Past Perfect
Past Continuous Changes to Past Perfect Continuous
Future Changes to Present Conditional
Future Continuous Changes to Conditional Continuous
Changes in Modals:
Can changes into Could, May changes into Might, Must changes into Had to/ would have to.
Modals that DO NOT Change: Would, Could, Might, Should, Ought to.
Practice questions
CAT exam: References to Study (Theory)
Advanced English grammar by Martin Hewings
https://www.wallstreetenglish.com/exercises/direct-and-indirect-speech-exercises
CAT exam: References to Study (Practice)
How to Prepare for Verbal Ability & Reading Comprehension for CAT by Meenakshi Upadhyay and Arun Sharma (9th Edition)
CAT Previous years Papers and Sample Papers.
Study Resources for CAT 2024
CAT Quantitative Aptitude Questions with Answers PDF | CAT 2024 GD PI Preparation: Experts and Toppers Tips |
Practice and remain focused; Day 32 will be posted tomorrow.
Frequently Asked Questions (FAQs)
Q: How can I determine Relative Speed?
A:
Relative speed lets you understand how quickly one thing moves in comparison to another. If two items are moving in the same direction, subtract their speeds. If they go in different directions, add their speeds.
Q: How long does it take two trains traveling in the same direction to pass one another?
A:
Put the following formula to use:
Where v1 > v2, time = (L1 + L2) / (v1 - v2).
Q: How do you figure out how long it will take two trains to cross one another while they are approaching one another?
A:
The formula used to determine the time taken is:
L1 and L2 = the train lengths
v1 and v2=the train speeds
Time = (L1 + L2) / (v1 + v2)
Q: What are Problems on Trains in the CAT Exam?
A:
Train problems include questions related to train speed, distance, and travel time. To answer these issues, apply the formula Distance = Speed × Time.
Q: What's the difference between direct and indirect VARC questions?
A:
Direct VARC questions gather basic information from an article, while indirect questions demand you determine the meaning or comprehend the author's intention. Both types need a thorough study of the passage.
Q: How can I determine Relative Speed?
A:
Relative speed lets you understand how quickly one thing moves in comparison to another. If two items are moving in the same direction, subtract their speeds. If they go in different directions, add their speeds.
Q: How long does it take two trains traveling in the same direction to pass one another?
A:
Put the following formula to use:
Where v1 > v2, time = (L1 + L2) / (v1 - v2).
Q: How do you figure out how long it will take two trains to cross one another while they are approaching one another?
A:
The formula used to determine the time taken is:
L1 and L2 = the train lengths
v1 and v2=the train speeds
Time = (L1 + L2) / (v1 + v2)
Q: What are Problems on Trains in the CAT Exam?
A:
Train problems include questions related to train speed, distance, and travel time. To answer these issues, apply the formula Distance = Speed × Time.
Q: What's the difference between direct and indirect VARC questions?
A:
Direct VARC questions gather basic information from an article, while indirect questions demand you determine the meaning or comprehend the author's intention. Both types need a thorough study of the passage.
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Have a question related to CAT ?
HELLO,
With an overall 98.54 percentile ( QA/DILR 97.55, VARC 94.89) and strong academics 9/9/0, you have a good profile. As a B.Tech candidate you can expect calls from :-
- IIM Shillong
- IIM Udaipur
- IIM Trichy
- IIM Ranchi
- IIM Raipur
- IIM Kashipur
- IIM Nagpur
- IIM Indore is Boderline
Hope this will help you !
Hello aspirant,
Your kid has a good profile even in the general category with a BTech from IIT Delhi, three years of excellent job experience in a leading industry, and a 96 percentile in the CAT. He has a strong chance at reputable MBA schools like IIM Shillong, IIM Udaipur, IIM Trichy, IIT Bombay, IIT Delhi, and others, depending on interview performance and profile match, even though the top IIMs often require higher percentiles.
Thank you
Hope it helps you
With an overall CAT percentile of 82.71 in CAT 2025 as a general category candidate, along with section-wise percentiles of 80.56 in VARC, 75.81 in DILR and 84.56 in QA, your chances at top IIMs are limited, as most older IIMs usually shortlist general category candidates at much higher percentiles. However, this percentile still keeps you eligible for admission calls from several Tier-2 and Tier-3 MBA colleges across India, especially those that consider overall performance, academic background and work experience along with CAT scores. You can expect calls from institutes such as IMT Nagpur, IMI Bhubaneswar, FORE School of Management (some programs), TAPMI Manipal (borderline), Great Lakes Institute of Management (Chennai or Gurgaon for PGPM/PGDM variants), K J Somaiya (depending on cut-offs), GIM Goa (through CAT or other exams), and state-level universities that accept CAT scores. Additionally, many good private universities and autonomous B-schools consider candidates in the 80–85 percentile range and conduct their own GD-PI rounds. To improve your chances, you should apply widely, prepare well for interviews, and highlight your academics, work experience, certifications and extracurricular achievements, as final selection is not based on CAT score alone.
All the best.
With an overall CAT 2025 percentile of 82.71, you are unlikely to get calls from the IIMs (including new or baby IIMs), as most of them generally shortlist candidates at 90+ percentile, even after considering category and profile factors. However, this percentile is still quite decent and opens doors to many good Tier-2 and Tier-3 MBA colleges in India that offer solid academics, reasonable placements, and good industry exposure.
At around 80–85 percentile, you have a strong chance of getting shortlisted by institutes such as IMI Bhubaneswar, IMT Nagpur, IMT Hyderabad, XIME Bangalore/Chennai, TAPMI Manipal (borderline, profile-dependent), IFMR GSB Krea University, FORE School of Management (certain programs), GIM Goa (specialised programs), LIBA Chennai (borderline), K J Somaiya Institute of Management (profile-based), Great Lakes Chennai/Gurgaon (PGDM – profile matters a lot), and Welingkar Mumbai (especially through profile + GDPI). Many reputed state universities and private institutes like PUMBA Pune, Delhi School of Management (DTU – if accepting CAT that year), BIMTECH (some programs), NDIM Delhi, ITM Navi Mumbai, and Jaipuria Institute of Management campuses are also realistic options.
Your sectional percentiles (VARC 80.56, DILR 75.81, QA 84.56) are fairly balanced, which works in your favor, as several colleges apply sectional cut-offs around 60–70 percentile. Final selection will depend not only on CAT score but also on academic background, graduation marks, work experience, diversity factors, and GD-PI performance. If you have work experience, it significantly improves your chances at colleges like Great Lakes, FORE, IFMR, and Welingkar.
In summary, while top IIMs are not achievable at 82.71 percentile, you can still secure admission into reputed mid-tier MBA colleges that provide good ROI and career growth if you perform well in the GD-PI process. It is advisable to apply broadly, focus on profile-based institutes, and prepare seriously for interviews to convert the best possible calls.
With 84.91 percentile in CAT (General, male, no work experience), top colleges like IIMs, IITs, FMS, MDI, etc. are not possible. You may get calls from private institutes such as IMT Nagpur/Hyderabad, IMI Bhubaneswar, XIME, SDMIMD, Welingkar (some programs) and similar colleges. Universities like Amity or LPU are also options.
It’s better to choose carefully, as placements and ROI may be average. Reattempting CAT or trying XAT/CMAT could improve options.
Popular CAT Questions
Directions for question :
M/s Deloitte Touche Tohmatsu Limited, one of the top four audit and accounting firms in the world with headquarters at London, UK, and with an operational presence in 153 countries, hires Management Trainees (MT) from all the premier management institutes of India thrice every year, in the months of January, May and September.
Each new group of Management Trainees (MT) have to go through a four month rigorous training schedule, after which they have to pass through a test consisting of a written assessment and a case-analysis. The top hundred ranked Management Trainees (MT) based on the performance in the test are confirmed as Management Executives (ME). The rest are given the opportunity of undergoing the training for four months one more time along with the next batch of Management Trainees (MT) and then passing through the subsequent test consisting of the written assessment and case-analysis. The Management Trainee (MT) who fails to get confirmed as a Management Executive (ME) the second time is fired.
The scatter-graph below depicts the number of Management Trainees (MT) at Deloitte taking the tests from January 2020 till May 2022, and the vis-à-vis hired Management Trainees (MT) at Deloitte who were fired :
It is also known that for the month of September 2019 at Deloitte, 96 hired Management Trainees (MT) failed to be confirmed as a Management Executive (ME) the first time, and that 36 hired Management Trainees (MT) were fired.
Question :
In which test did the minimum number of Management Trainees (MT) get confirmed as a Management Executive (ME) in the second attempt ?
Option: 1
September 2020
Option: 2
May 2021
Option: 3
January 2021
Option: 4
January 2022
Directions for question:
The bar-graph given below shows the foreign exchange reserves of Nepal (in million Rupees) from 2014 to 2021. Answer the following questions based on the graph :
Question:
What was the percentage increase (rounded to the nearest integer, if deemed necessary) in the foreign exchange reserves in 2020 over 2016 ?
Option: 1 None
Option: 2 None
Option: 3 None
Option: 4 None
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