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.
CAT Preparation Strategy Day 31
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.
CAT Preparation 2024 in 60 Days
Part-1: Quantitative Aptitude for CAT Exam
Important Concept/Formula Used in Relative Speedaptitude 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)
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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)
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.
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.
Since your payment status shows
"S"
, it means your payment is successful. The "payment unsuccessful" message on the form is likely a temporary system error or a delay in updating.
Do not make another payment.
Making a second payment could cause a double debit, which is difficult to get a refund for. You should:
Wait 24-48 hours
for the status to update automatically.
Download and save
a copy of your form and a screenshot of the "S" payment status as proof.
Check your bank statement
to confirm the money has been debited.
If the issue is not fixed after 48 hours,
contact the official CAT helpdesk
immediately with your transaction details.
The CAT 2025 exam is a national-level MBA entrance test for IIMs and top B-schools in India. It will be held on 30th November 2025 in computer-based mode across ~170 cities.
The registration is open from 1st August to 13th September 2025 on
iimcat.ac.in
.
Admit cards will be available from 5th November 2025 onward.
Graduates with at least 50 marks (45 for SC/ST/PwD) are eligible to apply.
The exam tests English, Reasoning, and Quantitative Aptitude in three timed sections.
With 305 marks in ICAR PG and being from ST category, your chances of getting an AIEEA (CAT) seat is good, especially in plant sciences and less competitive subjects
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 ?
Two friends Moloy and Niloy passed out from the Purulia Institute of Science and Technology with B.Tech degrees in Mechanical Engineering, but even after a year placement was hard to find. So they decided to take the challenge head-on, came down to Kolkata, rented a garage space on Park Street, and having an affinity towards making people enjoy good food, started their firm named 'B.Tech Bread-Omlette Wala'.
They started with three items on the menu. One was the French Toast which could be prepared in 3 minutes. The second was the Egg Tortillas which took 15 minutes to prepare. Any one of Moloy and Niloy could prepare any one of them at a time. The third was the Egg Bhurji with French Fries. This however was prepared on an automated fryer which could prepare 3 servings at a time and took 5 minutes irrespective of the number of servings equal to or below 3. The fryer did not need anyone to attend to it, and the time to put in the raw ingredients could be neglected. So one could tend to the preparation of other items while the Egg Bhurji with French Fries were being prepared.
They wanted to serve the orders as early as possible after the order was given. The individual items in any order were served as and when all the items were ready, and the order was then considered closed. None of the items on the menu were prepared in advance in anticipation of future orders.
On the first day, 3 groups of customers came in and ordered at 6.00 pm, 6.10 pm, and 6.13 pm. The first order was for a plate of Egg Tortillas, two plates of French Toast, and three plates of Egg Bhurji with French Fries. The second order was for a plate of French Toast and two plates of Egg Bhurji with French Fries. The third order was for a plate of Egg Tortilla and a plate of Egg Bhurji with French Fries.
On the backdrop of the above information answer the questions given :
Question:
Assuming that the next customer's order could only be attended to when the previous customer's order was closed, at what time would the first customer's order be considered closed ?
Six sticks of equal lengths were kept in the vertical position in an empty flower-vase, to be arranged at the six corners of a regular hexagon. The two ends of each of the sticks were of different colours.
The top ends of the sticks were one of each of the following colours – Red, Cyan, Pink, Brown, Black and Green. The bottom ends were one of each of the following colours – Blue, Yellow, White, Orange, Purple and Grey. Both the sets of colours mentioned were in no particular order.
It was also known that :
a) The stick with the red colour was opposite to the stick with the blue colour
b) There were exactly two sticks whose both ends had colours whose names started with the same letter
c) The stick with the grey colour was adjacent to the stick with the white colour
d) The stick with the cyan colour was adjacent to both the sticks with the brown colour and the one with the blue colour
e) The stick with the purple colour was adjacent to both the sticks with the grey colour and the one with the green colour
f) The stick with the white colour was opposite to the stick with the green colour
Question :
What was the colour of the bottom end of the stick having brown colour at the top end ?
Two friends Moloy and Niloy passed out from the Purulia Institute of Science and Technology with B.Tech degrees in Mechanical Engineering, but even after a year placement was hard to find. So they decided to take the challenge head-on, came down to Kolkata, rented a garage space on Park Street, and having an affinity towards making people enjoy good food, started their firm named 'B.Tech Bread-Omlette Wala'.
They started with three items on the menu. One was the French Toast which could be prepared in 3 minutes. The second was the Egg Tortillas which took 15 minutes to prepare. Any one of Moloy and Niloy could prepare any one of them at a time. The third was the Egg Bhurji with French Fries. This however was prepared on an automated fryer which could prepare 3 servings at a time and took 5 minutes irrespective of the number of servings equal to or below 3. The fryer did not need anyone to attend to it, and the time to put in the raw ingredients could be neglected. So one could tend to the preparation of other items while the Egg Bhurji with French Fries were being prepared.
They wanted to serve the orders as early as possible after the order was given. The individual items in any order were served as and when all the items were ready, and the order was then considered closed. None of the items on the menu were prepared in advance in anticipation of future orders.
On the first day, 3 groups of customers came in and ordered at 6.00 pm, 6.10 pm, and 6.13 pm. The first order was for a plate of Egg Tortillas, two plates of French Toast, and three plates of Egg Bhurji with French Fries. The second order was for a plate of French Toast and two plates of Egg Bhurji with French Fries. The third order was for a plate of Egg Tortilla and a plate of Egg Bhurji with French Fries.
On the backdrop of the above information answer the questions given :
Question:
Assuming that the next customer's order could only be attended to when the previous customer's order was closed, at what time would the third customer's order be considered closed ?
Two friends Moloy and Niloy passed out from the Purulia Institute of Science and Technology with B.Tech degrees in Mechanical Engineering, but even after a year placement was hard to find. So they decided to take the challenge head-on, came down to Kolkata, rented a garage space on Park Street, and having an affinity towards making people enjoy good food, started their firm named 'B.Tech Bread-Omlette Wala'.
They started with three items on the menu. One was the French Toast which could be prepared in 3 minutes. The second was the Egg Tortillas which took 15 minutes to prepare. Any one of Moloy and Niloy could prepare any one of them at a time. The third was the Egg Bhurji with French Fries. This however was prepared on an automated fryer which could prepare 3 servings at a time and took 5 minutes irrespective of the number of servings equal to or below 3. The fryer did not need anyone to attend to it, and the time to put in the raw ingredients could be neglected. So one could tend to the preparation of other items while the Egg Bhurji with French Fries were being prepared.
They wanted to serve the orders as early as possible after the order was given. The individual items in any order were served as and when all the items were ready, and the order was then considered closed. None of the items on the menu were prepared in advance in anticipation of future orders.
On the first day, 3 groups of customers came in and ordered at 6.00 pm, 6.10 pm, and 6.13 pm. The first order was for a plate of Egg Tortillas, two plates of French Toast, and three plates of Egg Bhurji with French Fries. The second order was for a plate of French Toast and two plates of Egg Bhurji with French Fries. The third order was for a plate of Egg Tortilla and a plate of Egg Bhurji with French Fries.
On the backdrop of the above information answer the questions given :
Question:
Suppose Moloy and Niloy had decided to process multiple orders at the same time, however strictly prioritising a first come first serve basis, when would the second customer's order be considered closed ?
Two friends Moloy and Niloy passed out from the Purulia Institute of Science and Technology with B.Tech degrees in Mechanical Engineering, but even after a year placement was hard to find. So they decided to take the challenge head-on, came down to Kolkata, rented a garage space on Park Street, and having an affinity towards making people enjoy good food, started their firm named 'B.Tech Bread-Omlette Wala'.
They started with three items on the menu. One was the French Toast which could be prepared in 3 minutes. The second was the Egg Tortillas which took 15 minutes to prepare. Any one of Moloy and Niloy could prepare any one of them at a time. The third was the Egg Bhurji with French Fries. This however was prepared on an automated fryer which could prepare 3 servings at a time and took 5 minutes irrespective of the number of servings equal to or below 3. The fryer did not need anyone to attend to it, and the time to put in the raw ingredients could be neglected. So one could tend to the preparation of other items while the Egg Bhurji with French Fries were being prepared.
They wanted to serve the orders as early as possible after the order was given. The individual items in any order were served as and when all the items were ready, and the order was then considered closed. None of the items on the menu were prepared in advance in anticipation of future orders.
On the first day, 3 groups of customers came in and ordered at 6.00 pm, 6.10 pm, and 6.13 pm. The first order was for a plate of Egg Tortillas, two plates of French Toast, and three plates of Egg Bhurji with French Fries. The second order was for a plate of French Toast and two plates of Egg Bhurji with French Fries. The third order was for a plate of Egg Tortilla and a plate of Egg Bhurji with French Fries.
On the backdrop of the above information answer the questions given :
Question:
Suppose Moloy and Niloy had decided to process multiple orders at the same time, however strictly prioritising a first come first serve basis, when would the third customer's order be considered closed ?
Two friends Moloy and Niloy passed out from the Purulia Institute of Science and Technology with B.Tech degrees in Mechanical Engineering, but even after a year placement was hard to find. So they decided to take the challenge head-on, came down to Kolkata, rented a garage space on Park Street, and having an affinity towards making people enjoy good food, started their firm named 'B.Tech Bread-Omlette Wala'.
They started with three items on the menu. One was the French Toast which could be prepared in 3 minutes. The second was the Egg Tortillas which took 15 minutes to prepare. Any one of Moloy and Niloy could prepare any one of them at a time. The third was the Egg Bhurji with French Fries. This however was prepared on an automated fryer which could prepare 3 servings at a time and took 5 minutes irrespective of the number of servings equal to or below 3. The fryer did not need anyone to attend to it, and the time to put in the raw ingredients could be neglected. So one could tend to the preparation of other items while the Egg Bhurji with French Fries were being prepared.
They wanted to serve the orders as early as possible after the order was given. The individual items in any order were served as and when all the items were ready, and the order was then considered closed. None of the items on the menu were prepared in advance in anticipation of future orders.
On the first day, 3 groups of customers came in and ordered at 6.00 pm, 6.10 pm, and 6.13 pm. The first order was for a plate of Egg Tortillas, two plates of French Toast, and three plates of Egg Bhurji with French Fries. The second order was for a plate of French Toast and two plates of Egg Bhurji with French Fries. The third order was for a plate of Egg Tortilla and a plate of Egg Bhurji with French Fries.
On the backdrop of the above information answer the questions given :
Question:
A fourth customer comes in and orders two plates of French Toast at 6.24 pm. Suppose Moloy and Niloy had decided to process multiple orders at the same time, however strictly prioritising a first come first serve basis. For exactly how many minutes would one of the friends be idle from 6.00 pm till serving the last customer, assuming that the four customers were the only ones to have come in within the period being discussed ?
Two friends Moloy and Niloy passed out from the Purulia Institute of Science and Technology with B.Tech degrees in Mechanical Engineering, but even after a year placement was hard to find. So they decided to take the challenge head-on, came down to Kolkata, rented a garage space on Park Street, and having an affinity towards making people enjoy good food, started their firm named 'B.Tech Bread-Omlette Wala'.
They started with three items on the menu. One was the French Toast which could be prepared in 3 minutes. The second was the Egg Tortillas which took 15 minutes to prepare. Any one of Moloy and Niloy could prepare any one of them at a time. The third was the Egg Bhurji with French Fries. This however was prepared on an automated fryer which could prepare 3 servings at a time and took 5 minutes irrespective of the number of servings equal to or below 3. The fryer did not need anyone to attend to it, and the time to put in the raw ingredients could be neglected. So one could tend to the preparation of other items while the Egg Bhurji with French Fries were being prepared.
They wanted to serve the orders as early as possible after the order was given. The individual items in any order were served as and when all the items were ready, and the order was then considered closed. None of the items on the menu were prepared in advance in anticipation of future orders.
On the first day, 3 groups of customers came in and ordered at 6.00 pm, 6.10 pm, and 6.13 pm. The first order was for a plate of Egg Tortillas, two plates of French Toast, and three plates of Egg Bhurji with French Fries. The second order was for a plate of French Toast and two plates of Egg Bhurji with French Fries. The third order was for a plate of Egg Tortilla and a plate of Egg Bhurji with French Fries.
On the backdrop of the above information answer the questions given :
Question:
Had Niloy been absent on that day, and assuming that the next customer's order could only be attended to when the previous customer's order was closed, at what time would the fourth customer's order (refer to the previous question) be considered closed ?
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 ?
The Jadavpur University’s Prince Anwar Shah Road hostel consists of two large separate buildings, one for the ladies and the other for the gents, while having a common kitchen and dining hall. It is the hostel of the CS and the EEC department of engineering students of the university.
In recognition of the growing dissatisfaction and hence complaints among the inmates of the hostel regarding the menu served for dinner, the Dean of the engineering department, Dr Aparesh Sanyal, personally decided to investigate the matter. He set about collecting information about the preference of dinner among the inmates, separately from the gents and the ladies wing of the hostel.
Dr Sanyal was able to gather the following partial information :
Hostel inmates
Menu preference for dinner
Total
Egg Meal
Fish Meal
Chicken Meal
Gents
20
Ladies
64
Total
60
The Warden of the hostel was consulted, who after investigation declared that the following facts were clear :
1. Forty percent of the hostel inmates were ladies
2. One-third of the gentlemen inmates preferred an egg meal for dinner
3. Half the hostel inmates preferred either fish meal or chicken meal
Question:
What proportion of the lady hostel inmates preferred a fish meal for dinner ?
A career as Marketing Director is also known as a marketing expert who is responsible for the overall marketing aspect of the company. He or she oversees plans and develops the company's budget. The marketing Director collaborates with the business team to plan and develop the marketing and branding strategies for the company's products or services.
A Business Development Executive identifies and pursues new business opportunities to drive company growth. They generate leads, build client relationships, develop sales strategies, and analyse market trends. Collaborating with internal teams, they aim to meet sales targets. With experience, they can advance to managerial roles, playing a key role in expanding the company’s market presence and revenue.
Content Marketing Specialists are also known as Content Specialists. They are responsible for crafting content, editing and developing it to meet the requirements of digital marketing campaigns. To ensure that the material created is consistent with the overall aims of a digital marketing campaign, content marketing specialists work closely with SEO and digital marketing professionals.
A Sales Manager leads a sales team to meet targets, formulates strategies, analyses performance, and monitors market trends. They typically hold a degree in management or related fields, with an MBA offering added value. The role often demands over 40 hours a week. Strong leadership, planning, and analytical skills are essential for success in this career.
A marketing manager is a person who oversees a company or product marketing. He or she can be in charge of multiple programmes or goods or can be in charge of one product. He or she is enthusiastic, organised, and very diligent in meeting financial constraints. He or she works with other team members to produce advertising campaigns and decides if a new product or service is marketable.
A Marketing manager plans and executes marketing initiatives to create demand for goods and services and increase consumer awareness of them. A marketing manager prevents unauthorised statements and informs the public that the business is doing everything to investigate and fix the line of products. Students can pursue an MBA in Marketing Management courses to become marketing managers.
An SEO Analyst is a web professional who is proficient in the implementation of SEO strategies to target more keywords to improve the reach of the content on search engines. He or she provides support to acquire the goals and success of the client’s campaigns.
Digital marketing is growing, diverse, and is covering a wide variety of career paths. Each job function aids in the development of effective digital marketing strategies and techniques. The aims and objectives of the individuals who opt for a career as a digital marketing executive are similar to those of a marketing professional: to build brand awareness, promote company services or products, and increase conversions. Individuals who opt for a career as Digital Marketing Executives, unlike traditional marketing companies, communicate effectively through suitable technology platforms.
Individuals who opt for a career as a business analyst look at how a company operates. He or she conducts research and analyses data to improve his or her knowledge about the company. This is required so that an individual can suggest the company strategies for improving their operations and processes.
In a business analyst job role a lot of analysis is done, things are learned from past mistakes and the successful strategies are enhanced further. A business analyst goes through real-world data in order to provide the most feasible solutions to an organisation. Students can pursue Business Analytics to become Business Analysts.
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