CAT Exam Breakthrough: Problems on Trains, Boat and Stream Questions For CAT Exam - Day 31

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

1. 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)

2. 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)

3. Concept of upstream:

Speed of boat in upstream = V_u = v – u

v = speed of boat in still water

u = speed of river/flow/current

4. Concept of downstream

Speed of boat in downstream = V_u = 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]

1. 6: 2

2. 7: 2

3. 25: 3

4. 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

1. seven digits.

2. at least two prime digits.

3. perfect squares as the first and the last digits.

4. 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.

5. 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.

6. 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.

7. 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.

8. 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.

1. 1778459

2. 4276891

3. 1367574

4. 9632578

5. 4556666

6. 4368579

7. 1366789

8. 9517531

9. 1573934

10. 964374

Solution:

Tip: Summarize the details given in the form of table:

Ans

1. A

2. A

3. E

4. E

5. C

6. A

7. B

8. D

9. E

10. 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

1. Changes in Tense

2. Changes in Person and Pronouns

3. Changes in Time Phrases

CAT Previous Years' MCQs on Direct and Indirect:

Question 1: Direct: He said, “Will you come for the meeting?”

Indirect:

1. He asked them whether he would come for the meeting.

2. He asked them that he will come for the meeting.

3. He said to them whether he will come for the meeting.

4. None of these

Ans: A

Explanation: Future tense changes to present conditional.

Question 2: Direct: She said, “I have baked a cake.”

Indirect:

1. She said that she baked a bake.

2. She said that she had baked a cake.

3. She said whether she had baked a cake.

4. 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)

• https://iim-cat-questions-answers.2iim.com/

• 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

Practice and remain focused; Day 32 will be posted tomorrow.