CAT 2026 Preparation: Day 11 – Loan Instalments, Ranking Questions and Past Tense Rules

Quantitative Aptitude For CAT 2026

Simple interest(SI) Instalments: Loans and instalments are key topics in financial mathematics and an essential tool to borrow money for various purposes, such as purchasing a home, financing education, or expanding a business.

When you take a loan from an agency and repay it in instalments after regular intervals, the amount returned at each interval is an instalment.

CAT Questions on Instalments and CAT Questions on Loans are categorised based on whether the interest rate is Simple Interest or Compound Interest.

We need to have a clear idea about how to calculate the Simple Interest or Compound Interest of a sum of money.

Simple Interest and Compound Interest

Simple Interest (SI)

$SI=\frac{P\times R\times T}{100}$

Compound Interest (CI)

$CI=P\left(1+\frac{R}{100}\right)^T-P$

Where:

• $P$ = Principal amount

• $R$ = Rate of interest per period (in percent)

• $T$ = Number of periods

Example: Calculating Equal Monthly Instalments at Simple Interest

Suppose Anil purchases a television worth ₹18,000 by paying a cash down payment of ₹10,000. He agrees to pay the remaining amount in six equal monthly instalments, with simple interest charged at 10% per month. Calculate the monthly instalment.

Step 1: Calculate the outstanding principal

Outstanding principal:

$P=18000-10000=₹8,000$

Step 2: Calculate the total debt after six months

Using the simple interest formula:

$SI=\frac{P\times R\times T}{100}$

Substituting the values:

$SI=\frac{8000\times10\times6}{100}=₹4,800$

Therefore, the total debt after six months is:

$A=P+SI$

$A=8000+4800=₹12,800$

Step 3: Calculate the equal monthly instalment

Let each monthly instalment be ₹$100x$.

The first instalment is paid after one month. Since this payment is made five months before the end of the six-month period, it reduces the final debt by the instalment amount plus the simple interest saved for those five months.

Similarly, each subsequent instalment reduces the final debt by the instalment amount plus the interest saved for the remaining months.

After all six instalments have been paid, the outstanding debt becomes zero.

Therefore,

$12800-(150x+140x+130x+120x+110x+100x)=0$

$12800-750x=0$

$750x=12800$

$x=\frac{12800}{750}\approx17.0667$

Since each instalment is ₹$100x$:

$100x\approx₹1,706.67$

Therefore, the monthly instalment is approximately ₹1,706.67.

Instalments at Simple Interest

To calculate the value of each equal annual instalment under simple interest, use the following formula:

$\text{Annual Instalment}=\frac{100A}{100T+\frac{RT(T-1)}{2}}$

Where:

• $A$ = Total debt due at the end of $T$ years, including simple interest

• $R$ = Annual interest rate (in percent)

• $T$ = Number of years

This formula applies when the debt is calculated for the full repayment period and equal annual instalments are paid at the end of each year.

Instalments At Compound Interest

Let a person take a loan from an agency at r% per annum compounded annually and pay the loan in equal instalments for n years.

Then, the amount due after $n$ years at a rate of $r%$ per annum, compounded annually, is:

$A=P\left(1+\frac{r}{100}\right)^n$

If the loan is repaid in $n$ equal annual instalments of $X$ each, paid at the end of every year, the amount due after $n$ years must equal the accumulated value of all the instalments.

$P\left(1+\frac{r}{100}\right)^n=X\left(1+\frac{r}{100}\right)^{n-1}+X\left(1+\frac{r}{100}\right)^{n-2}+\cdots+X\left(1+\frac{r}{100}\right)+X$

Where:

• $P$ = Principal loan amount

• $r$ = Annual compound interest rate (in percent)

• $n$ = Number of years

• $X$ = Amount of each annual instalment

• $A$ = Amount due after $n$ years

Questions and MCQs on Loans and advances , and CAT questions on instalments (SI and CI) can be divided into sub-categories during CAT preparation:

• Questions that involve calculations of the instalment value.

• Questions that include calculations of the interest rate charged.

• Questions that involve calculations of debt.

How to Solve CAT 2026 Loan and Instalment Questions Efficiently

Learn how to approach loan and instalment problems, choose the right calculation method, and avoid common errors in simple and compound interest questions.

Identify the Instalment Payment Timeline

Before solving a loan instalment question, identify the loan amount, interest rate, repayment frequency, and timing of each instalment. These details determine how interest is calculated and how much remains outstanding after every payment.

For example, if a borrower takes a loan of ₹50,000 and pays ₹10,000 as a down payment, the outstanding principal becomes ₹40,000, assuming the down payment is deducted before interest is charged. The interest calculation must then be based on the amount and repayment conditions specified in the question.

Choose the Right Approach for Different Instalment Questions

CAT loan and instalment questions can ask you to calculate the instalment amount, original debt, interest rate, or outstanding balance. Identify the unknown before forming an equation.

• To calculate the instalment: Express the total amount due and the repayments in terms of the unknown instalment.

• To calculate the original debt: Work backwards from the instalment amount and the stated interest conditions.

• To calculate the interest rate: Form an equation using the loan amount, repayment schedule, and instalments.

• To compare repayment plans: Calculate the total amount repaid under each plan, including interest.

Common Mistakes to Avoid in CAT 2026 Instalment Questions

1. Applying an annual interest rate directly to monthly periods without converting it appropriately.

2. Confusing the original loan amount with the outstanding principal.

3. Applying compound interest when the question specifies simple interest, or vice versa.

4. Ignoring whether instalments are paid at the beginning or end of a period.

5. Rounding intermediate calculations too early.

After solving, verify that the repayments settle the debt under the interest and timing assumptions stated in the question.

CAT 2026 Model Questions And Answers From CAT Previous Year Papers

Question 1. Equal Instalments at Compound Interest

John borrowed ₹2,10,000 from a bank at an interest rate of 10% per annum, compounded annually. The loan was repaid in two equal annual instalments, the first at the end of one year and the second at the end of two years. Find the amount of each instalment.

[CAT Question Paper 2018, TITA]

1. ₹1,21,000 (Correct answer)

2. ₹1,00,000

3. ₹1,20,000

4. ₹1,25,000

Solution:

Given:

• Principal, $P = ₹2,10,000$

• Annual interest rate, $r = 10\%$

• Number of instalments, $n = 2$

Let $X$ be the amount of each annual instalment.

The present value of the loan equals the sum of the present values of the two instalments.

$P=\frac{X}{1+r/100}+\frac{X}{(1+r/100)^2}$

Substituting the given values:

$210000=\frac{X}{1.1}+\frac{X}{1.21}$

Multiplying both sides by $1.21$:

$254100=1.1X+X$

$254100=2.1X$

$X=\frac{254100}{2.1}=121000$

Therefore, the correct answer is Option 1: ₹1,21,000.

Question 2. Three Equal Instalments at Compound Interest

Rahul takes a loan of ₹1,50,000 at an interest rate of 20% per annum, compounded annually. He agrees to repay the loan in three equal annual instalments, with each instalment paid at the end of each year. Find the amount of each instalment.

[CAT Sample Paper]

1. ₹71,209 (Correct answer, rounded to the nearest rupee)

2. ₹68,349

3. ₹76,484

4. ₹72,904

Solution:

Given:

• Principal, $P = ₹1,50,000$

• Annual interest rate, $r = 20\%$

• Number of instalments, $n = 3$

Let $X$ be the amount of each annual instalment.

The present value of the loan equals the sum of the present values of the three instalments.

$P=\frac{X}{1+r/100}+\frac{X}{(1+r/100)^2}+\frac{X}{(1+r/100)^3}$

Substituting the given values:

$150000=\frac{X}{1.2}+\frac{X}{1.44}+\frac{X}{1.728}$

Taking the LCM of the denominators:

$150000=\frac{180X+150X+125X}{216}$

$150000=\frac{455X}{216}$

Therefore,

$X=\frac{150000\times216}{455}$

$X\approx \text{₹}71,208.79$

Rounding to the nearest rupee gives ₹71,209.

Therefore, the correct answer is Option 1: ₹71,209.

Question 3. Calculating Debt from Equal Instalments at Simple Interest

What is the amount of debt that can be discharged in six equal annual instalments of ₹800 each if the debt is due in six years at 5% simple interest per annum?

[CAT Sample Paper]

1. ₹6,600

2. ₹7,500

3. ₹8,000

4. ₹5,400 (Correct answer)

Solution:

Given:

• Annual instalment, $I = ₹800$

• Simple interest rate, $r = 5\%$

• Number of years, $t = 6$

Let the original debt be $P$.

For equal annual instalments under simple interest, the formula is:

$I=\frac{100P}{100t+\frac{rt(t-1)}{2}}$

Substituting the given values:

$800=\frac{100P}{100(6)+\frac{5(6)(6-1)}{2}}$

Simplifying the denominator:

$800=\frac{100P}{600+75}$

$800=\frac{100P}{675}$

Rearranging:

$P=\frac{800\times675}{100}$

$P=\text{₹}5,400$

Therefore, the correct answer is Option 4: ₹5,400.

Prerequisite For CAT Questions On Instalments

To prepare for this topic for the CAT exam, students must know of

1. Fractions and percentages at fingertips.

2. Successive Changes

3. Simple Interest and Compound Interest

References to Study (Theory)

• Quantitative Aptitude for CAT by N.K. Sinha

• Dinesh Miglani Tutorials for CAT, IPM, CLA, T SSC, BANK

Logical Reasoning And Data Interpretation:

Ranking (LR)

Ranking is the process of determining the position or place of a person or thing based on comparison and other information given in the questions for the CAT exam.

It is one of the most essential parts of Logical Reasoning for the CAT exam.

Ranking-based reasoning questions require students to determine the relative positions of people or objects using the information provided. To solve these questions, students should understand how to calculate positions from opposite ends, determine the total number of people in a row, identify the number of people between two positions, and solve problems involving swapped positions. Careful reading, logical deduction, and the use of simple diagrams can improve accuracy.

Ranking: Question Types Asked In the CAT Exam

There are many different types of questions asked in the CAT exam based on the ranking.

Some of them are:

1. The position or ranking of the person is asked from the bottom, left, right, or top.

2. Questions based on the swapping of positions.

3. Questions are based on the number of persons between two positions.

4. Questions based on finding the total number of objects or persons.

Approaches And Tips To Solve The CAT Question Paper On Ranking

1. The total number of persons in a row = (sum of positions of the same person from both sides) - 1
   Example: Sunil is 16th from either end of a row; the total number of persons in the row = 16 + 16 - 1 = 31

2. If the position of a person/ object from one end is n, and the total number of persons/objects in the row is m; then the position of the same person from the other end will be (m - n + 1).

3. While calculating the number of places between two persons, cases of overlapping and non-overlapping should be treated differently.

4. Analyse the given information in the question by thorough reading.

5. Use visualisation/imagination skills.

6. Try to draw all the possibilities and eliminate the wrong ones.

Questions On Ranking (LR) From CAT Previous Year Papers

These questions can help you build the concept of ranking: (Based on the CAT exam):

Question 1. Ranking in a Queue

In a queue of 50 people, Antara is 19th from the front, while Manthara is 28th from the back. Lolita is exactly midway between Antara and Manthara. What position does Lolita occupy from the front? [CAT Sample Paper]

1. 20th

2. 19th

3. 18th

4. 21st

Solution:

Manthara's position from the front = 50 − 28 + 1 = 23rd.

Number of people between Antara and Manthara = 23 − 19 − 1 = 3.

Since Lolita is exactly midway between them, she must be the 21st from the front.

Therefore, the correct answer is Option 4: 21st.

Question 2. Interchanging Positions

In a row of boys, Ritesh is 7th from the right end, and Manish is 9th from the left end. After they interchange their positions, Ritesh occupies the 27th position from the left. How many boys are present in the row?

1. 35

2. 26

3. 33

4. 34

Solution:

After the interchange, Ritesh occupies Manish's original position, which is 9th from the left. Since Ritesh is now 27th from the left, the total number of boys is determined by the fact that Ritesh's original position was 7th from the right and Manish's original position was 9th from the left.

Total number of boys = 27 + 7 − 1 = 33.

Therefore, the correct answer is Option 3: 33.

Question 3. Arranging People in a Row

Five friends, A, B, C, D, and E, are sitting in a row facing north. A is immediately to the right of B and immediately to the left of C. D is immediately to the right of E and immediately to the left of B. Who is sitting in the middle?

1. A

2. B

3. C

4. D

Solution:

From the given conditions:

• A is immediately to the right of B and immediately to the left of C. Therefore, the sequence is B – A – C.

• D is immediately to the right of E and immediately to the left of B. Therefore, the sequence is E – D – B – A – C.

The complete arrangement is E – D – B – A – C.

Therefore, B is sitting in the middle.

The correct answer is Option 2: B.

Question 4. Ranking by Marks

In a class of 40 students, there are 10 boys and 30 girls. Ramesh is ranked 12th overall when students are arranged in descending order of marks. Among the boys, he is ranked 7th. How many girls are ranked above him?

1. 4

2. 5

3. 6

4. 7

Solution:

Ramesh is ranked 12th overall, so 11 students are ranked above him.

He is ranked 7th among the boys, meaning 6 boys are ranked above him.

Number of girls ranked above Ramesh = Total students ranked above him − Boys ranked above him

= 11 − 6

= 5

Therefore, the correct answer is Option 2: 5.

Prerequisite For CAT Preparation:

To prepare the questions based on the Ranking for CAT 2026, a student must know:

• Basic Additions and Subtractions

• Sequence and Series

References to Study (Practice):

• Verbal and Non-Verbal Reasoning by R.S.S. Aggarwal. (Basic)

• LRDI for CAT and GMAT by Nishit K Sinha. (Advance)

• CAT previous year papers and CAT sample paper

Advanced Ranking and Position-Based Reasoning for CAT 2026

Explore systematic methods to solve complex ranking problems involving position constraints, relative order, and swapping, with techniques to improve accuracy.

Solve Ranking Questions Using Position Constraints

Some ranking questions provide several conditions involving relative positions, immediate neighbours, or changes in positions. Instead of trying to solve every condition mentally, represent the people or objects using numbered positions.

For example, if A is immediately to the left of B, treat their positions as a fixed pair. Place this pair first and then arrange the remaining people according to the other conditions. This reduces confusion when several relationships are involved.

Pay particular attention to expressions such as:

• Immediately before or after

• Exactly two people between two individuals

• To the left or right of a particular person

• Two people exchanging positions

Use a Case-Based Approach for Complex Ranking Problems

Sometimes the available information does not determine a single arrangement immediately. In such cases, consider the possible arrangements separately and eliminate those that contradict the conditions.

1. Record the fixed positions and immediate-neighbour relationships.

2. Identify conditions that allow more than one arrangement.

3. Create separate cases for those possibilities.

4. Check each case against every condition.

5. Select the arrangement that satisfies all the information given.

This approach is particularly useful when a question combines multiple people, relative order, and position changes.

VARC Topic: -Tenses Part-2 (Past Tense)

As discussed in the previous article, tenses are divided into three types for easy CAT preparation. Today, we will discuss the Past Tense.

The past tense is used to describe the event that has occurred in the Past.

Past Tense can further be divided into four categories to indicate the action as follows:

The simple past tense describes an action that was completed in the past. The time of the action may be mentioned or understood from the context.

Formula: Subject + Verb (Past Form) + Object

Example: Geetha studied at the Indian Institute of Management (IIM) Ahmedabad.

2. Past Perfect Tense

The past perfect tense describes an action that was completed before another action or event in the past.

Formula: Subject + Had + Verb (Past Participle) + Object

Example: Kushal noticed that Barsha had left her mobile behind.

3. Past Continuous Tense

The past continuous tense describes an action that was in progress at a particular time in the past or when another action occurred.

Formula: Subject + Was/Were + Verb-ing + Object

Example: Sneha was eating pizza when her friend arrived.

4. Past Perfect Continuous Tense

The past perfect continuous tense describes an action that had been continuing for a period of time before another event or point in the past.

Formula: Subject + Had Been + Verb-ing + Object

Example: I had been preparing for this examination for five months before the exam date was announced.

Students can practice with simple past tense worksheets and read simple past tense formulas to gain a better understanding of basic past tense examples.

CAT questions on Past tense and Past participle from the Previous year's papers

Question 1. I met the director yesterday, and he assured me that he will help if you ask him. [Sentence Correction]

[CAT Previous Year Papers]

1. I met the director yesterday, and he assured me that he will help if you ask him.

2. I met the director yesterday, and he assured me that he would help if you asked him.

3. I met the director yesterday, and he assured me that he would help if you ask him.

4. No correction required.

Solution:

Correct answer: Option 2.

The sentence refers to a past conversation, indicated by “met” and “assured.” In reported speech, “will” generally changes to “would,” and “ask” may change to “asked” when the condition is also reported from a past perspective.

Therefore, Option 2 is the most appropriate answer among the given options.

Question 2. The Chief Proctor entered the classroom to see what the students __________. [Fill in the Blanks]

1. had been doing

2. was doing

3. had been done

4. were doing

Solution:

Correct answer: Option 4.

The sentence describes an action that was in progress when the Chief Proctor entered the classroom. Therefore, the past continuous tense is appropriate.

The correct sentence is: “The Chief Proctor entered the classroom to see what the students were doing.”

• Option 1: “Had been doing” is past perfect continuous. It generally emphasises an action that had been continuing before another past event.

• Option 2: “Was doing” is incorrect because “students” is plural; the correct form is “were doing.”

• Option 3: “Had been done” is passive in construction and does not fit the intended meaning.

• Option 4: “Were doing” correctly uses the past continuous tense with the plural subject “students.”

Prerequisite For Tenses:

• Basic Knowledge of Verbs and their forms.

• Knowledge of the use of helping verbs (Was/Were/had/had been)

• Knowledge of Nouns/Pronouns.

Tips For Error Correction In Past Tenses:

• Learn the rules of all types of past tenses.

• Read good Newspapers that use correct grammar (like The Hindu).

• Do basic exercises on the past tense.

• Attempt Mock-Tests.

References to Study (Theory):

• How to Prepare for Verbal Ability & Reading Comprehension for CAT by Meenakshi Upadhyay and Arun Sharma (9th Edition)

• Learn English with Rebecca · engVid (YouTube Channel)

• Class (VI-VIII) NCERT for basic grammar rules.

Past Tense and Reported Speech Rules for CAT 2026 VARC

Understand the sequence of past events, reported speech rules, and common grammatical errors to strengthen your English grammar for CAT 2026.

Understand the Sequence of Past Events

When a sentence describes two events that occurred in the past, the tense should make their sequence clear. The past perfect is commonly used for an action that happened before another past event.

Example:

Incorrect: When the examination started, I already completed my revision.

Correct: When the examination started, I had already completed my revision.

The revision was completed before the examination started, so the past perfect clarifies which event occurred first.

However, the past perfect is not compulsory whenever a sentence mentions two past events. If the sequence is already clear, the simple past may also be appropriate.

Apply Backshift Rules in Reported Speech

In reported speech, the tense often shifts back when the reporting verb is in the past.

Universal truths generally remain in the present tense even when reported using a past-tense reporting verb.

CAT 2026 Day 11 Revision Plan and Self-Assessment

Follow a focused revision schedule for Quantitative Aptitude, Logical Reasoning, and VARC, and use an error log to identify weaknesses and improve performance.

Follow a Focused Revision Schedule

After completing the concepts and solved examples, use the following schedule to revise the three topics covered in Day 11.

This is a suggested 75-minute revision session, separate from the time required to study the complete article or attempt additional questions.

Maintain an Error Log for CAT 2026 Preparation

An error log helps identify recurring weaknesses and makes revision more targeted. After each practice session, record:

1. The question type in which you made a mistake.

2. Whether the mistake was conceptual, computational, or caused by misreading.

3. The correct method or grammatical rule.

4. What you need to do to avoid repeating the error.

For example, if you calculate an instalment incorrectly because you misinterpret when the first payment is due, record the timing error and revise that concept before attempting similar questions.

Improve Accuracy Before Increasing Speed

Begin by solving questions independently and checking both the final answer and the method. In quantitative aptitude and logical reasoning, verify that your answer satisfies the original conditions. In grammar, ensure that you can explain why the selected sentence is correct.

Once your accuracy improves, attempt similar questions under a time limit. This will help you develop a consistent approach to the different sections of the CAT 2026 preparation roadmap.

CAT 2026 Preparation Resources

Find CAT 2026 preparation eBooks, previous years’ question banks, sample papers, topic-wise practice questions, and revision plans in one place. Download these resources to strengthen your VARC, DILR, and Quantitative Aptitude preparation and improve your exam readiness.

Practice, stay focused, and wait for the CAT strategy to prepare for Day 12 (Practice Set-3) tomorrow.

Thank You

All the best.