Quantitative Aptitude Topics Explained with Examples and Solutions#
Below is a simple, exam-ready explanation of each major quantitative aptitude topic, including clear examples and step-by-step solutions.
1. Number System#
Definition: Deals with types, properties, and rules of numbers: natural numbers, integers, fractions, etc.
Example Question: Which of the following is an even number: 6, 9, 13, 17?
Solution: Even numbers are divisible by 2.
- 6 ÷ 2 = 3 (even) Answer: 6 is an even number.
2. HCF & LCM#
Definition:
- HCF (Highest Common Factor): Largest number dividing two or more numbers.
- LCM (Lowest Common Multiple): Smallest number divisible by given numbers.
Example Question: Find the HCF and LCM of 12 and 18.
Solution:
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 18: 1, 2, 3, 6, 9, 18 HCF = 6
Multiples of 12: 12, 24, 36, 48… Multiples of 18: 18, 36, 54… LCM = 36
3. Ratio & Proportion#
Definition:
- Ratio: Comparison of two quantities (e.g., 2:3).
- Proportion: Equality of two ratios (e.g., 2:3 = 4:6).
Example Question: Divide ₹1200 between A and B in the ratio 2:3.
Solution:
- Total parts = 2 + 3 = 5
- A’s share = (2/5) × 1200 = ₹480
- B’s share = (3/5) × 1200 = ₹720
4. Percentages#
Definition: A fraction or ratio out of 100.
Example Question: What is 25% of 200?
Solution: 25% of 200 = (25/100) × 200 = 50
5. Average#
Definition: The sum of all values divided by the number of values.
Example Question: Find the average of 5, 8, 10.
Solution: Average = (5 + 8 + 10) / 3 = 23 / 3 = 7.67
6. Profit & Loss#
Definition: Related to buying and selling goods.
Formulas:
- Profit = Selling Price (SP) – Cost Price (CP)
- Loss = CP – SP
Example Question: Item bought for ₹100, sold for ₹120. Profit %?
Solution: Profit = 120 – 100 = ₹20 % Profit = (Profit / CP) × 100 = (20/100) ×100 = 20%
7. Simple & Compound Interest#
Simple Interest (SI): SI = (P × R × T) / 100 (P = principal, R = rate, T = years)
Compound Interest (CI): CI = P × [(1 + R/100)^T – 1]
Example Question: Find SI on ₹1,000 at 8% for 2 years.
Solution: SI = (1000 × 8 × 2) / 100 = 160
8. Simplification#
Definition: Simplifying arithmetic expressions using BODMAS rules.
Example Question: Solve: 8 + 4 × 2
Solution: According to BODMAS (Multiplication before Addition): = 8 + (4 × 2) = 8 + 8 = 16
9. Time & Work#
Definition: Problems involving work done by people or machines.
Example Question: A can do a job in 12 days, B in 8 days. How long together?
Solution: A’s 1 day work = 1/12; B’s = 1/8 Combined work/day = 1/12 + 1/8 = (2 + 3)/24 = 5/24 Total days = 24/5 = 4.8 days
10. Time, Speed & Distance#
Formula: Speed = Distance / Time
Example Question: If a car travels 120km in 3hr, what is its speed?
Solution: Speed = 120km / 3hr = 40km/hr
11. Fractions & Decimals#
Definition:
- Fraction: Part of a whole (e.g., 3/4)
- Decimal: Fraction in decimal format (e.g., 0.75)
Example Question: Convert 3/8 to decimal.
Solution: 3 ÷ 8 = 0.375
12. Data Interpretation#
Definition: Analyzing data given in tables, graphs, charts.
Example Question: Table: Students in Classes
| Class | No. of Students |
|---|---|
| A | 40 |
| B | 50 |
What is the total number of students?
Solution: Total = 40 + 50 = 90
Quick Tips#
- Practice each concept with examples.
- Memorize key formulas.
- Learn shortcuts for calculations.
- Practice with previous year questions for speed and accuracy.
By understanding theory and solving standard questions, you will confidently tackle the Quantitative Aptitude section in exams.