Verbal Logic Framework

Arithmetic Reasoning

Verbal Reasoning Study Mode

Arithmetic Reasoning

🔍 Master systematic approaches to break down complex problems. Learn pattern recognition, logical deduction, and strategic thinking frameworks.

2 Exercises
30 Minutes
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Verbal Logic Framework

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Logical Framework – Arithmetic Reasoning

The Logical Framework of Arithmetic Reasoning is based on transforming real-world mathematical situations into structured numerical equations and solving them step-by-step using logical analysis and arithmetic concepts.

Arithmetic Reasoning combines:

  • Logical interpretation
  • Numerical analysis
  • Equation formation
  • Formula application
  • Step-by-step reasoning

Core Structure of Arithmetic Reasoning

Read the Question
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        ▼
Identify Given Information
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Determine What is Asked
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        ▼
Convert into Mathematical Form
        │
        ▼
Apply Appropriate Formula
        │
        ▼
Perform Calculations
        │
        ▼
Verify Final Answer

Step 1 – Understand the Problem Carefully

The first and most important step is understanding the actual meaning of the question.

Example:

A car travels 180 km in 3 hours. Find the speed.

Given:

  • Distance = 180 km
  • Time = 3 hours

Required:

Speed

Step 2 – Extract Important Data

Arithmetic Reasoning questions usually contain extra words. Identify only useful numerical information.

Question:

Ravi bought 12 books for ₹600 and sold them equally among his friends. Find the cost of one book.

Important Data:

  • Total books = 12
  • Total cost = ₹600

Step 3 – Convert Words into Mathematical Form

The next step is translating verbal statements into equations.

Example:

“25% of a number is 50”

Mathematical Form:

25/100 × x = 50

Step 4 – Apply Appropriate Formula

Choose the correct arithmetic formula based on the problem type.

Problem Type Formula
Percentage (Value ÷ Total) × 100
Average Sum ÷ Number of Terms
Speed Distance ÷ Time
Profit Selling Price − Cost Price
Simple Interest (P × R × T) ÷ 100
Ratio Comparison of Quantities

Step 5 – Solve Systematically

Perform calculations carefully in a logical sequence.

Example:

Find the average of 10, 20, and 30.

Step 1:

Sum = 10 + 20 + 30 = 60

Step 2:

Average = 60 ÷ 3

Average = 20

Step 6 – Verify the Final Answer

Always verify whether the final answer satisfies the original question.

Verification helps avoid:

  • Calculation mistakes
  • Unit conversion errors
  • Wrong formula application
  • Incorrect interpretation

Logical Framework for Ratio Problems

Ratio problems compare two or more quantities proportionally. 

Identify Ratio
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Assign Variables
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Form Equation
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Solve Variable
      │
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Find Required Quantity

Example – Ratio Framework

Question:

The ratio of Rahul and Aman’s ages is 3 : 5. Their age difference is 12 years. Find Aman’s age.

Assume:

Rahul = 3x

Aman = 5x

Difference:

5x − 3x = 12

2x = 12

x = 6

Aman’s age = 5 × 6 = 30 years

Logical Framework for Percentage Problems

Percentage problems involve proportional comparisons. 

Identify Total Quantity
        │
        ▼
Convert Percentage into Fraction
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        ▼
Apply Formula
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        ▼
Solve Required Value

Example – Percentage Framework

Question:

If 20% of a number is 40, find the number.

20/100 × x = 40

x = 40 × 100 ÷ 20

x = 200

Logical Framework for Time & Distance

These problems involve relationships between speed, time, and distance. 

Speed = Distance / Time

Distance = Speed × Time

Time = Distance / Speed

Example – Time & Distance Framework

Question:

A train travels 240 km in 4 hours. Find the speed.

Speed = Distance ÷ Time

240 ÷ 4

Speed = 60 km/h

Logical Framework for Probability

Probability measures the likelihood of an event occurring. 

Probability =
Favorable Outcomes
──────────────────
Total Outcomes

Example – Probability Framework

Question:

What is the probability of getting a head when a coin is tossed once?

Favorable outcomes = 1

Total outcomes = 2

Probability = 1/2

Most Important Arithmetic Reasoning Areas

Topic Exam Importance
Percentages Very High
Ratio & Proportion Very High
Average High
Profit & Loss High
Time & Distance Very High
Probability Moderate

Common Mistakes in Arithmetic Reasoning

  • Ignoring units during calculations
  • Applying incorrect formulas
  • Misreading percentage values
  • Calculation errors
  • Skipping verification step
  • Incorrect interpretation of word problems

Quick Solving Strategy

  1. Read carefully.
  2. Identify required quantity.
  3. Extract important numerical data.
  4. Convert into equation form.
  5. Apply correct formula.
  6. Solve step-by-step.
  7. Verify final answer.

Final Takeaway

The Logical Framework of Arithmetic Reasoning is based on converting verbal mathematical situations into structured equations and solving them using arithmetic concepts and logical thinking.

Strong understanding of formulas, numerical relationships, and systematic problem-solving techniques helps candidates solve Arithmetic Reasoning questions quickly and accurately in competitive examinations.

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