Cheatsheet: Arithmetic Ability | IBPS PO Prelims & Mains Preparation - Bank Exams PDF Download

Theory

Arithmetic Ability is a crucial part of the Quant section in Banking Entrance exams. Understanding the fundamentals and formulas is essential for solving problems accurately and quickly. A solid grasp of basic operations, percentages, fractions, ratios, and time-related problems will greatly enhance problem-solving efficiency.

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Tips

• The order of division and multiplication can be interchanged. Similarly, the order of addition and subtraction can be interchanged.

• For fractions, find a common denominator when adding or subtracting, and use reciprocals when dividing.

• For time and work problems, the combined work is calculated using the formula 1 / (1/x + 1/y).

• In percentage problems, always express the part and whole clearly before calculating.

Formula

1. Basic Operations

   • Addition: Combine numbers to get a total.

   • Subtraction: Find the difference between two numbers.

   • Multiplication: Repeated addition of a number.

   • Division: Splitting a number into equal parts.

2. Percentages

   • Formula:
     Percentage = (Part/Whole) × 100

   • To Find Percentage of a number:
     Percentage of number = (Percentage × Number) ÷ 100

   • Increase/Decrease:
     New Value = Original Value ± (Percentage × Original Value) ÷ 100

3. Fractions

   • Addition/Subtraction: Find a common denominator and then add or subtract the numerators.

   • Multiplication: Multiply numerators together and denominators together.

   • Division: Multiply by the reciprocal of the second fraction.

4. Averages

   • Formula:
     Average = (Sum of all values) ÷ (Number of values)

   • To find the Average Speed:
     Average Speed = Total Distance ÷ Total Time

5. Speed, Time, and Distance

   • Formula:
     Speed = Distance ÷ Time
     Time = Distance ÷ Speed
     Distance = Speed × Time

   • Units:
     Distance = Kilometers (km), Time = Hours (hr), Speed = Kilometers per hour (km/h)

6. Profit and Loss

   • Profit:
     Profit = Selling Price (SP) - Cost Price (CP)

   • Loss:
     Loss = Cost Price (CP) - Selling Price (SP)

   • Profit Percentage:
     Profit Percentage = (Profit ÷ Cost Price) × 100

   • Loss Percentage:
     Loss Percentage = (Loss ÷ Cost Price) × 100

7. Simple Interest

   • Formula:
     SI = (Principal × Rate × Time) ÷ 100

   • Amount (A):
     Amount = Principal + Simple Interest

8. Compound Interest

   • Formula:
     Amount = P (1 + r/n)^(nt)

     • P = Principal,

     • r = Rate of interest,

     • n = Number of times interest is compounded per year,

     • t = Time in years

   • Compound Interest (CI) = Amount - Principal

9. Ratio and Proportion

   • Ratio: Expresses a relationship between two quantities.

   • Proportion: An equation stating that two ratios are equal.

   • Formula for Direct Proportion:
     a/b = c/d → a × d = b × c

   • Formula for Inverse Proportion:
     a × b = c × d

10. Partnership

    • Profit Sharing:
      Profit Share = (Investment of Partner) ÷ (Total Investment)

11. Algebraic Formulas

    • (a + b)² = a² + 2ab + b²

    • (a - b)² = a² - 2ab + b²

    • (a + b)(a - b) = a² - b²

12. Work and Time

    • Formula:
      Work = Rate × Time

    • If A can do a job in x days, and B in y days, the combined work is done in:
      1/(1/x + 1/y) days

13. Mixtures and Alligations

    • Alligation Formula:
      (Cost Price of First Item - Mean Price) / (Mean Price - Cost Price of Second Item)

14. Time and Work

    • If A completes a task in x days and B completes it in y days, the time taken by A and B together is:
      (x × y) / (x + y)

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