Business Mathematics and Statistics
This domain checks numerical accuracy in commercial arithmetic (percentage, profit and loss, simple and compound interest, ratio) and in basic statistics (averages, dispersion, index numbers). Show the formula, substitute, then compute - examiners award step marks.
Core rules
- Simple interest: SI = P × R × T ÷ 100.
- Compound interest: A = P(1 + R/100)^n, CI = A − P.
- Percentage change = (New − Old) ÷ Old × 100.
- Mean = sum of values ÷ number of values; median = middle value of data arranged in order; mode = most frequent value.
- Compounding half-yearly: halve the rate and double the periods.
Worked example
₹8,000 is invested at 10% for 2 years. SI = 8,000 × 10 × 2 ÷ 100 = ₹1,600. CI: A = 8,000(1.10)² = 8,000 × 1.21 = ₹9,680, so CI = ₹1,680. The ₹80 gap is exactly 10% of the first year's interest (₹800 × 10% = ₹80) - compound interest pays interest on interest, which is why CI always exceeds SI for the same rate and term beyond one year.
Worked elasticity check (economics overlap)
Price falls from ₹10 to ₹8 and quantity rises from 100 to 150 units: % change in quantity = 50%, % change in price = 20%, so elasticity = 50 ÷ 20 = 2.5, i.e. elastic, and total revenue rises from ₹1,000 to ₹1,200.
Traps that cost marks
- Using T in months instead of years when the rate is per annum.
- Forgetting to halve the rate and double the periods for half-yearly compounding.
- Finding the median without first arranging the data in ascending order.
- Confusing a percentage rise with a percentage-point rise.