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# 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.