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PRERNA FOR IAS
MATH FORMULA
(CSAT)
1. Percentage
Percentage represents a part of a whole expressed out of 100. It is calculated as:
Percentage = (Value ÷ Total Value) × 100
Percentages are widely used in examinations, business, statistics, finance, and everyday calculations. They help compare quantities easily and measure increases, decreases, profits, losses, and overall performance.
2. Average
Average, also called the arithmetic mean, represents the central value of a set of observations. It is calculated by dividing the total sum by the number of observations.
Average = Sum of Observations ÷ Number of Observations
Average helps summarize data and is widely used in statistics, economics, and education.
3. Ratio
A ratio compares two quantities of the same kind. It is expressed as a:b or a/b. Ratios help show relationships between quantities and are commonly used in mathematics, business, maps, and daily life. Simplifying ratios makes comparisons easier and more meaningful for analysis.
4. Proportion
A proportion is an equality between two ratios, written as a:b = c:d. It shows that two ratios represent the same relationship. Proportions are useful in scaling, maps, recipes, and solving mathematical problems involving direct and indirect comparisons between quantities.
5. Simple Interest
Simple Interest is the interest calculated only on the principal amount.
SI = (P × R × T) ÷ 100
where P is principal, R is rate of interest, and T is time. It is commonly used in banking, loans, and financial calculations involving fixed interest rates.
6. Speed
Speed measures how fast an object moves.
Speed = Distance ÷ Time
It is usually measured in kilometers per hour (km/h) or meters per second (m/s). Speed is an important concept in transportation, physics, and daily life, helping determine travel time and movement efficiency.
7. Profit and Loss
Profit occurs when the selling price exceeds the cost price, while loss occurs when the cost price is higher than the selling price.
Profit = SP – CP
Loss = CP – SP
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Master essential math formulas for CSAT: percentage, average, ratio, simple interest, quadratic equations, geometry, and logarithms with clear explanations.
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