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2.1 BASIC ARITHMETIC
Explanation
Basic arithmetic consists of the four fundamental operations used in everyday calculations. These operations test accuracy, speed, and understanding of number relationships.
Arithmetic Operations Summary Table
| Operation | Formula | Meaning |
|---|---|---|
| Addition | a + b | Combining quantities |
| Subtraction | a − b | Finding difference |
| Multiplication | a × b | Repeated addition |
| Division | a ÷ b | Equal sharing |
Worked Examples
Example 1: Addition
Question:
Find the total number of travelers if 245 entered in the morning and 378 entered in the afternoon.
Solution:
245 + 378
= 623
Answer: 623 travelers
Example 2: Subtraction
Question:
If 560 passengers arrived and 185 departed, how many remain?
Solution:
560 − 185
= 375
Answer: 375 passengers remain
Example 3: Multiplication
Question:
Each bus carries 48 passengers. How many passengers are in 9 buses?
Solution:
48 × 9
= 432
Answer: 432 passengers
Example 4: Division
Question:
360 travelers are to be processed equally by 12 officers. How many travelers per officer?
Solution:
360 ÷ 12
= 30
Answer: 30 travelers per officer
2.2 PERCENTAGES
Explanation
A percentage expresses a number as a fraction of 100. It is widely used in reports, statistics, and comparisons.
Formula
Percentage = (Part ÷ Whole) × 100
Worked Examples
Example 1
Question:
Out of 200 applicants, 50 passed the aptitude test. Find the percentage that passed.
Solution:
Percentage = (50 ÷ 200) × 100
= 0.25 × 100
= 25%
Answer: 25% passed
Example 2
Question:
What is 15% of 400?
Solution:
15% = 15 ÷ 100
15% of 400
= (15 ÷ 100) × 400
= 60
Answer: 60
Example 3
Question:
A report shows that 30% of 1,200 travelers were foreigners. How many foreigners were recorded?
Solution:
= (30 ÷ 100) × 1200
= 360
Answer: 360 foreigners
2.3 RATIOS
Explanation
A ratio compares quantities of the same type and shows their relative sizes.
Ratio Format
a : b
Worked Examples
Example 1: Simplifying a Ratio
Question:
The ratio of male officers to female officers is 48 : 32. Simplify.
Solution:
HCF of 48 and 32 = 16
48 ÷ 16 = 3
32 ÷ 16 = 2
Simplified ratio = 3 : 2
Example 2: Applying a Ratio
Question:
The ratio of officers to civilians is 5 : 3. If there are 120 officers, how many civilians are there?
Solution:
5 parts = 120
1 part = 120 ÷ 5 = 24
Civilians = 3 × 24
= 72
Answer: 72 civilians
2.4 FRACTIONS
Explanation
Fractions represent parts of a whole and are commonly tested through simplification and operations.
Fraction Structure
Numerator / Denominator
Worked Examples
Example 1: Simplifying a Fraction
Question:
Simplify 18 / 54
Solution:
GCD of 18 and 54 = 18
18 ÷ 18 = 1
54 ÷ 18 = 3
Simplified fraction = 1 / 3
Example 2: Addition of Fractions
Formula:
a/b + c/d = (ad + bc) / bd
Question:
2/5 + 3/10
Solution:
Common denominator = 10
2/5 = 4/10
4/10 + 3/10 = 7/10
Answer: 7/10
Example 3: Multiplication of Fractions
Formula:
(a/b) × (c/d) = (a × c) / (b × d)
Question:
4/7 × 7/9
Solution:
Numerator: 4 × 7 = 28
Denominator: 7 × 9 = 63
28/63 = 4/9
Answer: 4/9
2.5 WORD PROBLEMS
Explanation
Word problems test understanding of real-life numerical situations and correct application of formulas.
Steps
-
Read carefully
-
Identify known values
-
Identify required value
-
Apply formula
-
Solve
Worked Examples
Example 1: Speed
Question:
A patrol vehicle travels 180 km in 4 hours. Find its speed.
Formula:
Speed = Distance ÷ Time
Solution:
Speed = 180 ÷ 4
= 45 km/h
Answer: 45 km/h
Example 2: Time
Question:
A bus travels at 60 km/h for a distance of 300 km. How long does the journey take?
Formula:
Time = Distance ÷ Speed
Solution:
Time = 300 ÷ 60
= 5 hours
Answer: 5 hours
2.6 NUMERICAL PATTERNS & SEQUENCES
Explanation
Patterns test your ability to recognize logical numerical relationships.
Worked Examples
Example 1: Arithmetic Sequence
Sequence:
5, 10, 15, 20, ___
Difference = +5
Next term = 20 + 5
= 25
Example 2: Geometric Sequence
Sequence:
3, 6, 12, 24, ___
Rule: Multiply by 2
Next term = 24 × 2
= 48
Example 3: Mixed Pattern
Sequence:
2, 6, 12, 20, ___
Differences:
+4, +6, +8
Next difference = +10
Next term = 20 + 10
= 30
