Business Mathematics (B.Com 1st Year)
1. Ratio and Proportion
Ratio shows the relationship between two quantities, while proportion shows equality of two ratios.
Important Formulas
Ratio of a to b = a : b
a : b = c : d ⇒ ad = bc
Continued proportion: a : b = b : c ⇒ b² = ac
2. Percentage
Percentage is a way of expressing a number as a fraction of 100. It is widely used in profit–loss, interest, and statistics.
Important Formulas
Percentage = (Part / Whole) × 100
Increase % = (Increase / Original Value) × 100
Decrease % = (Decrease / Original Value) × 100
3. Profit, Loss and Discount
This topic is essential for understanding trade, pricing, and business transactions.
Important Formulas
Profit = Selling Price (SP) − Cost Price (CP)
Loss = Cost Price (CP) − Selling Price (SP)
Profit % = (Profit / CP) × 100
Loss % = (Loss / CP) × 100
Discount = Marked Price (MP) − Selling Price (SP)
Discount % = (Discount / MP) × 100
4. Simple Interest
Simple Interest is calculated on the principal amount for the entire period.
Important Formulas
Simple Interest (SI) = (P × R × T) / 100
Amount (A) = P + SI
Where:
P = Principal
R = Rate of Interest per annum
T = Time (in years)
5. Compound Interest
Compound Interest is calculated on the principal plus accumulated interest.
Important Formulas
Amount: A = P (1 + R/100)^T
Compound Interest (CI) = A − P
6. Time and Work
This topic deals with efficiency and work completion, useful in production planning.
Important Formulas
Work = Rate × Time
If A can do a work in x days, then A’s 1 day work = 1/x
Combined work: 1/x + 1/y
7. Time, Speed and Distance
Used in transportation, logistics, and scheduling problems.
Important Formulas
Speed = Distance / Time
Distance = Speed × Time
Time = Distance / Speed
8. Permutation and Combination
This topic is useful in probability and decision-making.
Important Formulas
Permutation: nPr = n! / (n − r)!
Combination: nCr = n! / [r! (n − r)!]
9. Matrices and Determinants
Matrices are used in economics, statistics, and business models.
Important Formulas
Addition of matrices: A + B
Multiplication: AB (only if columns of A = rows of B)
Determinant of 2×2 matrix:
|a b| |c d| = ad − bc
10. Linear Equations
Linear equations help in solving business problems involving demand, supply, and cost.
Important Formulas
For equations:
a₁x + b₁y = c₁
a₂x + b₂y = c₂
Solution:
x = (c₁b₂ − c₂b₁) / (a₁b₂ − a₂b₁)
y = (a₁c₂ − a₂c₁) / (a₁b₂ − a₂b₁)
