Arithmetic Reasoning
About This Cheat Sheet
Your complete guide to Arithmetic Reasoning for competitive exams. This cheat sheet helps you solve mathematical problems quickly using logical reasoning and shortcut techniques.
๐ Age & Number Problems
- Present, Past & Future Ages
- Ratio-Based Age Problems
- Finding Numbers from Conditions
- Digit & Consecutive Numbers
- Average & Weighted Average
- Missing Number Problems
๐ Ratio & Proportion
- Simple Ratio
- Compound Ratio
- Direct Proportion
- Inverse Proportion
- Partnership & Profit Sharing
- Capital & Time Ratio
โฑ๏ธ Speed & Work Problems
- Speed-Time-Distance
- Relative Speed
- Average Speed
- Individual Work
- Combined Work
- Pipes & Cisterns
๐ฐ Profit, Loss & Interest
- Cost Price & Selling Price
- Discount & Marked Price
- Profit & Loss Percentage
- Simple Interest
- Compound Interest
- Successive Percentage
๐งฎ Advanced Topics
- Mixture & Alligation
- Alligation Rule
- Replacement Problems
- Perimeter, Area & Volume
- Percentage Increase/Decrease
- Population Problems
๐ Exam Categories
- SSC & Banking
- Railways & UPSC
- CAT & MBA Entrance
- Defence & Insurance
- Placement Tests
- Other Competitive Exams
๐ Speed ร Time
= Distance
Speed Formula๐ Rate ร Time
= Work
Work Formula๐ฐ Profit
= SP โ CP
Profit Formula๐ Average
= Sum รท Count
Average Formula๐ Key Formulas Reference
โฑ๏ธ Time & Work
- Work = Rate ร Time
- 1/A + 1/B = Combined Rate
- Pipes: Inlet - Outlet
- Efficiency = 1/Time
- If A does work in X days: Rate = 1/X
๐ฐ Profit & Loss
- Profit = SP โ CP
- Loss = CP โ SP
- Profit% = (Profit/CP) ร 100
- Discount = MP โ SP
- SP = CP ร (100 + P%)/100
๐ Interest & Average
- SI = (PรRรT)/100
- CI = P(1+R/100)^T - P
- Average = Sum of terms / N
- Weighted Avg = ฮฃ(wรx)/ฮฃw
- Speed = Distance/Time
๐ Age Problems
๐ข Number Problems
๐ Ratio & Proportion Examples
๐ Simple Ratio
- Ratio: a : b = c : d
- Example: 2 : 3 = 4 : 6
- Cross Multiply: aรd = bรc
- 2ร6 = 3ร4 = 12 โ
๐ Direct Proportion
- If y โ x: y = kx
- Example: y = 2x
- When x=3, y=6
- As x increases, y increases
๐ Inverse Proportion
- If y โ 1/x: xy = k
- Example: xy = 12
- When x=3, y=4
- As x increases, y decreases
๐ Quick Reference: Key Formulas
โฑ๏ธ Time & Work
- Work = Rate ร Time
- 1/A + 1/B = Combined Rate
- Pipes: Inlet - Outlet
- Efficiency = 1/Time
๐ฐ Profit & Loss
- Profit = SP โ CP
- Loss = CP โ SP
- Profit% = (Profit/CP) ร 100
- Discount = MP โ SP
๐ Interest & Average
- SI = (PรRรT)/100
- CI = P(1+R/100)^T - P
- Average = Sum / N
- Weighted Avg = ฮฃ(wรx)/ฮฃw
๐ฏ Smart Ways to Approach Arithmetic Reasoning
The Golden Rule: In arithmetic reasoning, identify the core mathematical relationship first, then apply the appropriate formula. Don't rush โ a careful approach saves time in the long run.
Step-by-Step Approach:
- Step 1: Read the problem carefully and identify what's given
- Step 2: Identify what needs to be found (the unknown)
- Step 3: Choose the right formula or method
- Step 4: Apply the formula with correct values
- Step 5: Verify your answer for logical consistency
Common Mistakes to Avoid:
- โ Skipping the problem statement and rushing to solve
- โ Applying the wrong formula (e.g., CI instead of SI)
- โ Confusing direct and inverse proportions
- โ Forgetting to convert units (km/h โ m/s, hours โ minutes)
Proven Strategy: The "Formula Bank" technique โ keep a mental list of key formulas. Before starting any question, identify which formula category it belongs to (time-work, speed-distance, profit-loss, etc.). This helps you choose the right approach quickly.
Memory Trick: Remember these key formulas:
- ๐ Speed ร Time = Distance
- ๐ Rate ร Time = Work
- ๐ Profit = SP โ CP
- ๐ Average = Sum รท Count
๐ก Pro Tips for Arithmetic Reasoning
โ Learn Key Formulas
Memorize all essential formulas โ they save valuable time during exams
โ Identify the Topic First
Recognize which formula category the problem belongs to
โ Use Shortcut Techniques
Learn Vedic math and other shortcuts for faster calculations
โ Practice with Timers
Time yourself โ speed is crucial in competitive exams
Download Cheat Sheet
This cheat sheet has 2 pages. Choose download option:
Preview
Still have questions?
We're here to help! Reach out to our support team for any queries.