CAT 2025 Exam Success: Mastering Loans, Installments, Ranking, and Past Tense Made Easy- Day 11

Quantitative Aptitude For CAT 2025

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 = (Principal × Rate × Time) / 100

Compound interest = Principal × [1 + (Rate / 100)]Time – Principal

Suppose Anil purchased a television worth Rs. 18000 paying Rs. 10000 cash down payment, and every month a fixed instalment has to be paid for the next 6 months, where interest is charged at 10% per month on simple interest.

You need to calculate the EMI value.

First, you need to calculate the debt (the Amount due after 6 months if paid in a single time)

Principal = 18000 – 10000 = Rs. 8000

Debt = 8000 + (8000 × 10 × 6)/100 = Rs. 12800

First instalment after 1st month = Rs. 100x (Let)

Amount due after 1 month = Rs. 12800 – 100x – 100x × 5 × 10/100 = Rs. 12800 – 150x

(The instalment amount and Interest for 5 months have to be subtracted from the amount due since 100x is returned after one month and interest is added for 6 months in the original amount due)

Amount due after 2 months = Rs. 12800 – 150x – 100x – 100x × 4 × 10/100

= Rs. 12800 – 290x

(The instalment amount and Interest for 4 months have to be subtracted from the amount due since 100x is returned after two months, and interest is added for 6 months in the original amount due)

Amount due after 3 months = Rs. 12800 – 290x – 100x – 100x × 3 × 10/100

= Rs. 12800 – 420x

(The instalment amount and Interest for 3 months have to be subtracted from the amount due since 100x is returned after three months and interest is added for 6 months in the original amount due)

Amount due after 4 months = Rs. 12800 – 420x – 100x – 100x × 2 × 10/100

= Rs. 12800 – 540x

(Instalment amount and Interest for 2 months have to be subtracted from the amount due since 100x is returned after four months, an interest is added for 6 months in the original amount due)

Amount due after 5 months = Rs. 12800 – 540x – 100x – 100x × 1 × 10/100

= Rs. 12800 – 650x

(The instalment and Interest for 1 month have to be subtracted from the amount due since 100x is returned after five months, and interest is added for 6 months in the original amount due)

Amount due after 6 months = Rs. 12800 – 650x – 100x

(The instalment amount has to be subtracted from the amount, but interest is not subtracted since 100x is returned after six months and interest is added for 6 months in the original amount due)

After payment of all instalments, the amount due = 0

So, Rs. $12800 – 650x – 100x = 0$

⇒ $x = 17.067$

⇒ $100x =$ Rs. $1706.7$

Instalments At Simple Interest

To find the value of the annual instalment with Simple Interest, we use the following formula:

Annual instalment = $\frac{100A}{100T} + \left[\frac{RT(T - 1)}{2}\right]$

Where A is the total amount to be paid in T years with R% annual interest.

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 value of each instalment can be calculated by the given formula:

Amount due after n years = $P \left(1 + \frac{r}{100}\right)^n$

If paid in instalments, the amount due must be equal to

$P \left(1 + \frac{r}{100}\right)^n = X \left(1 + \frac{r}{100}\right)^{n-1} + X \left(1 + \frac{r}{100}\right)^{n-2} + X \left(1 + \frac{r}{100}\right)^{n-3} + \cdots + X \left(1 + \frac{r}{100}\right)$

Where, X = Instalment value

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.

We need to further study topics such as “instalment loans for bad credit”, “instalment loan calculator”, and “loan instalment payment” to delve deeper into this chapter. Now we will practice some instalment loan example questions to better understand the topic.

CAT 2025 Model Questions And Answers From CAT Previous Year Papers

Question 1. John borrowed Rs. 2,10,000 from a bank at an interest rate of 10% per annum, compounded annually. The loan was repaid in two equal instalments, the first after one year and the second after another year. The first instalment was the interest of one year plus part of the principal amount, while the second was the rest of the principal amount plus due interest thereon. Then each instalment, in Rs., is:

[CAT Question Paper 2018, TITA]

1. Rs. 121000 (Correct answer)

2. Rs. 100000

3. Rs. 120000

4. Rs. 125000

Solution:

P = 210000, n = 2, r = 10

Let X be the value of the instalment each year.

Using,

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

$\Rightarrow 210000 \left(1 + \frac{10}{100}\right)^2 = X \left(1 + \frac{10}{100}\right)^1 + X$

$\Rightarrow 210000 \cdot \frac{121}{100} = X \cdot \frac{11}{10} + X$

$\Rightarrow 2100 \cdot 121 = X \cdot \frac{21}{10}$

$\therefore X = 121000$

Hence, the correct answer is Rs. 121000.

Question 2. Rahul takes a loan of Rs 150000 at an interest rate of 20% compound interest, which is compounded annually. He agrees to pay three equal instalments in three years, one instalment at the end of every year. Find the value of each instalment.

[CAT Question Paper - sample paper]

1. Rs. 71209 (Correct answer)

2. Rs. 68349

3. Rs. 76484

4. Rs. 72904

Solution:

P = 150000, n = 3, r = 20

Let X be the value of the instalment each year.

Using,

$P \left(1 + \frac{r}{100}\right)^n = X \left(1 + \frac{r}{100}\right)^{n-1} + X \left(1 + \frac{r}{100}\right)^{n-2} + X \left(1 + \frac{r}{100}\right)^{n-3} + \cdots + X \left(1 + \frac{r}{100}\right)$

$\Rightarrow 150000 \left(1 + \frac{20}{100}\right)^3 = X \left(1 + \frac{20}{100}\right)^2 + X \left(1 + \frac{20}{100}\right) + X$

$\Rightarrow 150000 \cdot \frac{216}{125} = X \cdot \frac{36}{25} + X \cdot \frac{6}{5} + X$

$\Rightarrow 150000 \cdot \frac{216}{125} = X \cdot \frac{91}{25}$

$\therefore X = 71209$

Hence, the correct answer is Rs. 71209.

Question 3: What is the amount (in INR) of debt that will be discharged in 6 equal instalments of INR 800 each, if the debt is due in 6 years at 5% per annum?

[CAT Question Paper - sample paper]

1. Rs. 6600

2. Rs. 7500

3. Rs. 8000

4. Rs. 5400 (Correct answer)

Solution:

Given:

Instalment = INR 800

Rate, r = 5%

Time, t = 6 years

Let the debt be x.

Instalment = (Debt × 100) / [100t + {r × t(t-1)} / 2]

⇒ 800 = 100x / [100 × 6 + {5 × 6(6-1)}/2]

⇒ 800 = 100x / 675

∴ x = 5400

Hence, the correct answer is Rs. 5400.

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

References to Study (Practice)

• Arun Sharma: A Quantitative Approach for CAT (7th Edition)

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

• CAT previous year papers and CAT sample paper

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.

For some information about this topic, students can study “Ranking logical reasoning pdf”, “order and ranking Logical Reasoning ” and “Ranking logical reasoning questions”.

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. In a queue, Antara is 19th from the front, while Manthara is 28th from the back, and Lolita is just in the middle of the two. Consider that there are 50 people in the queue. What position does Lolita occupy from the front? [CAT sample paper]

1. 20th

2. 19th

3. 18th

4. 21st (Correct answer)

Solution:

Total persons sitting between Antara and Manthara = 50 – 19 – 28 = 3

Lolita is in the middle of the two; So, Antara and Lolita have just one person between them. Therefore, Lolita must be on the 21st from the front.

Question 2. In a row of boys, Ritesh and Manish occupy the 7th place from the right end and the 9th place from the left end, respectively. Now, if they interchange their places, Ritesh and Manish occupy 25th place from the right and 27th place from the left, respectively. How many boys are present in the row?

1. 35

2. 26

3. 33 (Correct answer)

4. Cannot be determined

Solution:

Ritesh's Position from the right end = 7; Now Manish occupies the position of Ritesh, which is 27th from the left.

So, total number of boys = 7 + 27 – 1 = 33

Question 3: Five friends, A, B, C, D, and E, are sitting in a row facing north. A is to the immediate right of B and immediate left of C. D is to the immediate right of E and immediate 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 right of B → B, A, C (because A is immediately left of C)

• D is immediately correct of E and immediately left of B → E, D, B, A, C.

Therefore, B is in the middle.

Question 4: In a class of 40 students, there are 10 boys and 30 girls. Ramesh is ranked 12th 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 and 7th among the boys.

So, there are six boys ranked higher than him.

Therefore, the number of girls ranked above him is 11 - 6 = 5

Prerequisite For CAT Preparation:

To prepare the questions based on the Ranking for CAT 2025, a student must know:

• Basic Additions and Subtractions

• Sequence and Series

References to Study (Theory):

• Verbal and Non-Verbal Reasoning by R.S. Aggarwal.

• 2IIM CAT Preparation (YouTube Channel)

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

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:

• Simple Past Tense/ Past Indefinite Tenses: A habitual action in the past. The action has already taken place in the past, but the exact time of the the action is not definite.
  Formula: Subject + Verb (Past tense) + Object
  Example: Geetha studied at the Indian Institute of Management (IIM) Ahmedabad.

• Past Perfect Tense: It refers to an action that happened before another event.
  Formula: Subject + Had + Verb (Past participle) + Object
  Example: Kushal noticed that Barsha had left his mobile behind.

• Past Continuous Tense: Continuous action in the past, that happened for some time.
  Formula: Subject + Was/ Were + Verb (Present participle) + Object
  Example: Sneha was eating pizza.

• Past Perfect Continuous Tense: denotes an action that was in progress before another event in the past.
  Formula: Subject + Had been + Verb (Present participle) + Object
  Example: I had been preparing for this examination for five months.

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

3. Met the director yesterday, and he assured me that he would help if you asked him.

4. No correction required

Solution:
The correct answer is Option B.

With ‘yesterday’, the Past indefinite tense should be used. So, option A is incorrect.

Option (c) is wrong because in “he will help if you ask him”, the verb 'will help' is in the future, which is the result of a condition ‘if you ask’, and both cannot be in the future.

Question 2. The Chief Proctor entered the classroom to see what the students_________. [Fill in the blanks]

1. Go had been doing

2. Went, was doing

3. Gone, had been doing

4. Went, we're doing

Solution:

The correct answer is option D.

Past indefinite with past continuous tense (For progressive work) is to be used.

Option A is wrong because “The chief proctor” is singular. So “goes” is appropriate for the past form.

Option B is wrong because “students” is plural, so “were doing” should be appropriate.

Option C is wrong because the past participle form of a verb alone can’t be used. There has to be a has/have/had.

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.

References to Study (Practice):

• engvid.com (Web)

• Wren and Martin (sixth edition)

• Practice CAT Sample Papers

Free eBooks for CAT Preparation 2025

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

Thank You

All the best.