Quantitative aptitude

1. Basic Aptitude Class
3-Hour Session | Fundamentals
& Problem-Solving

2. Agenda for the Session
Introduction to Aptitude
Number System
Bodmas
HCF & LCM
Percentages
Ratio & Proportion
Time & Work
Time, Speed & Distance
Simple & Compound Interest
Practice Questions & Discussion

3. Introduction to Aptitude
✅ Competitive Exams
✅ Job Interviews
Why Aptitude
📌 Used in Banking, SSC,
UPSC, CAT, GATE, and job
tests.
📌 Helps pick the best
candidates.
📌 Improves thinking speed
and accuracy.

4. Number Series Puzzle 1️
1️
⃣
Find the missing number:
2, 6, 12, 20, 30, ?
Odd One Out ❌
2️
⃣
Which word does not belong to the group?
Apple, Mango, Banana, Carrot, Grape
Quick Math Trick ➕
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Without a calculator, can you solve this in 5
seconds?
999 × 1001 = ?

5. BODMAS
BODMAS is an acronym that helps you
remember the order of operations in math. It
stands for:
➢ B: Brackets
➢ O: Of
➢ D: Division
➢ M: Multiplication
➢ A: Addition
➢ S: Subtraction

6. BODMAS
1. 45-(28-(37-(15-p))) = 58
2. [(18 – 6) ÷ 4] + [72 – 12 ÷ 3 of 2]
3. 12 + 6 × 27 ÷ 3 + 2 – 16 ÷ 8 × 2
4. 8 ÷ 4 × (6 + 2 of 4) + 32 – 2

7. Number System Basics
➢Natural Numbers, Whole Numbers and
Integers
➢ Even & Odd Numbers, Prime &
Composite Numbers
➢ Divisibility Rules (2,3,4,5,9,11)

8. Natural Numbers (N) 1️
1️
⃣
● Definition: Counting numbers starting from 1.
● Examples: 1, 2, 3, 4, 5, ... (goes on infinitely)
Whole Numbers (W) 🔢
2️
⃣
● Definition: Natural numbers including zero.
● Examples: 0, 1, 2, 3, 4, 5, ...
Integers (Z) ➖➕
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● Definition: All positive and negative whole numbers,
including zero.
● Examples: ... -3, -2, -1, 0, 1, 2, 3 ...

9. Identify the Number Type
1️
1️
⃣
Which of the following numbers are natural numbers, whole numbers, and integers?
a) -5
b) 0
c) 7
d) 12
e) -3
True or False
2️
⃣
a) All natural numbers are whole numbers.
b) All whole numbers are natural numbers.
c) All integers are whole numbers.
d) Zero is a natural number.
Find the Missing Number
3️
3️
⃣
Fill in the missing number in the series:
-5, -3, -1, __, 3, 5
Smallest and Largest
4️
⃣
a) What is the smallest natural number?
b) What is the smallest whole number?
c) What is the smallest integer?

10. HCF & LCM
➢ HCF: Highest Common Factor (GCD)
➢ LCM: Least Common Multiple
➢ Methods: Prime Factorization & Division Method
➢Application in real-life problems

11. What is LCM (Least Common Multiple)?
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● The smallest number that is divisible by two or
more given numbers.
● Example: LCM of 4 and 6
Multiples of 4 → 4, 8, 12, 16, 20...
Multiples of 6 → 6, 12, 18, 24...
LCM = 12 (smallest common multiple).

12. What is HCF (Highest Common Factor)?
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The largest number that divides two or more
numbers exactly.
Example: HCF of 18 and 24
Factors of 18 → 1, 2, 3, 6, 9, 18
Factors of 24 → 1, 2, 3, 4, 6, 8, 12, 24
HCF = 6 (highest common factor).

13. LCM and HCF Formula
📌 LCM × HCF = Product of Numbers
When to Use This Formula?
● If LCM and one number are given, you can find the
other number.
● If HCF and LCM are given, you can find the product
of the numbers.
Example Application:
If LCM of two numbers is 120 and HCF is 6, and one
number is 24, find the second number.

14. Find the Missing Number
1️
1️
⃣
The HCF of two numbers is 4, and their LCM is 120. If one of the numbers is
24, find the second number.
Verify the Formula
2️
⃣
The LCM and HCF of two numbers are 180 and 15, respectively. The two
numbers are 45 and x. Find x and verify the formula.
Application-Based Question
3️
3️
⃣
Two numbers have a product of 1440. Their HCF is 12. Find their LCM.
Word Problem
4️
⃣
The LCM of two numbers is 840, and their HCF is 14. If one number is 84, find
the second number.
Challenge Question
5️
5️
⃣
The product of two numbers is 4800. If their HCF is 20, find their LCM.

15. Percentages Basics
➢Converting fractions to percentages &
vice versa
➢Percentage increase/decrease
➢Example: If a price increases by 20%,
find the new price.

16. Percentage Estimation Game 1️
1️
⃣
Question:
You go shopping, and a shirt costs 1000
₹ . There’s a
30% discount.
Without using a calculator, estimate the final price!
💡 Hint: Break it down:
10% of 1000 =
₹ 100
₹
30% = ?

17. Quick Percentage Riddle 2️
2️
⃣
Question:
What is 50% of 50% of 200?
a) 25
b) 50
c) 100
d) 200
Fastest Thinker Challenge ⏳
3️
⃣
Fill in the blanks without calculating!
1. 25% of 200 = ___
2. 50% of 80 = ___
3. 10% of 500 = ___
4. 75% of 40 = ___

18. Real-Life Challenge 🏆
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If you scored 80% on a test with 50 questions, how
many did you get right?
Trick Question 🎭
If a number is increased by 25% and then decreased
by 25%, does it return to the original number? 🤔

19. Where do we use percentages?
➢ Shopping Discounts 🛒
➢ Exam Scores 🎓
➢ Salary Hikes 💰
➢ Population Growth/Decline 📉
Example:
"A shirt originally costs 2000 and has a 20%
₹
discount. What is the final price?"
💡 Solution:
● 20% of 2000 = (20/100) × 2000 = 400
₹ ₹
● Final Price = 2000 - 400 = 1600
₹ ₹ ₹

20. 1 ️
1️⃣What is 25% of 300?
2️⃣A student's marks increased from 40 to 50.
Find the percentage increase.
3 ️
3️⃣A mobile phone was 10,000, but after a
₹
15% discount, what is the new price?
4️⃣A population decreased by 10% from 5000.
What is the new population?
5 ️
5️⃣If a price increases by 50% and then
decreases by 50%, does it return to the
original?

21. What is a Ratio?
A ratio is a way of comparing two quantities of the
same kind. It tells us how many times one value is
compared to another.
📌 Formula:
Ratio = First Quantity/Second Quantity
a : b
Ratio and Proportion

22. 📌 Examples:
1. In a class, there are 30 boys and 20 girls. The
ratio of boys to girls is:
Boys: Girls
= 30:20
= 3:2
2. A recipe requires 2 cups of sugar and 3 cups of
flour. The ratio of sugar to flour is:
2:3

23. 📌 Real-Life Applications of Ratios:
➢ Mixing ingredients in cooking 🍲
➢ Speed (distance:time) in km/hr 🚗
➢ Comparing students’ marks in exams 📚

24. What is Proportion?
A proportion shows that two ratios are equal.
📌 Formula:
a : b = c : d
a/b = c/d
or written as
a : b :: c : d
📌 Example:
If 2 pens cost 10, how much will 4 pens cost?
₹
2 : 10 = 4 : x
2 / 10 = 4 / x
✅ Answer: 4 pens will cost 20.
₹

25. Time & Work
• Work efficiency concept
• Formula: Work = Efficiency × Time
• Example: A can do a task in 10 days, B in 15 days. How
long together?

26. 1. A does a work in 10 days and B does the
same work in 15 days. In how many days
they together will do the same work?
2. A, B and C can complete a piece of work in
24, 6 and 12 days respectively. Working
together, they will complete the same
work in:

27. Time, Speed & Distance
Formula:
Speed = Distance/Time

28. Time, Speed & Distance
Unit Conversion:
➢ 1 km/h = (5/18) m/s
➢ 1 m/s = (18/5) km/h
Basic Speed Calculation
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Q1: A car covers 240 km in 4 hours. What is its speed?
Speed = Distance / Time
= 240 / 4
=60 km/hr

29. Time, Speed & Distance
Finding Time
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Q2: A train is moving at 90 km/h. How much time will it
take to cover 180 km?
✅ Solution:
Time = Distance / Speed
= 180 / 90
= 2 hours

30. Time, Speed & Distance
Finding Distance
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Q3: A bike moves at 40 km/h for 2.5 hours. Find the
total distance traveled.
✅ Solution:
Distance = Speed×Time
=40×2.5
d = 100 km

31. Simple Interest
SI Formula:
SI = (P × R × T) / 100
● SI = Simple Interest
● P = Principal (Initial Amount)
● R = Rate of Interest (per annum)
● T = Time (in years)

32. Simple Interest
Q1: Find the Simple Interest on 5000 for 3 years at
₹
an interest rate of 5% per annum.
✅ Solution:
SI= ( 5000 × 5×3 ) / 100
= 75000 / 100
= 750
₹

33. Simple Interest
Q2: A person borrows 8000 at 6% per annum for 4
₹
years. What is the total amount to be paid?
✅ Solution:
SI = (8000×6×4) / 100
=192000 / 100
= 1920
₹
Total Amount = P + SI
A = 8000+1920
= 9920
₹

34. Simple Interest
Q2: A person borrows 8000 at 6% per annum for 4
₹
years. What is the total amount to be paid?
✅ Solution:
SI = (8000×6×4) / 100
=192000 / 100
= 1920
₹
Total Amount = P + SI
A = 8000+1920
= 9920
₹

35. Simple Interest
Q1: Find the simple interest on 6000 for 2 years at a
₹
rate of 5% per annum.
Q2: A man deposits 8000 in a bank at 7% per annum
₹
for 3 years. How much interest will he earn?
Q3: A loan of 12,000 is taken for 4 years at 6% simple
₹
interest. What will be the total amount to be paid at
the end of 4 years?

36. Summary & Conclusion
• - Key Formulas Recap
• - Common Shortcuts
• - Q&A Session
• - Homework Practice Problems