Fundamentals of Business Mathematics
Business mathematics is the arithmetic engine reused throughout Paper 3: ratio and proportion, percentage, simple and compound interest, annuities, counting principles (permutations and combinations) and standard series. Questions usually hide the formula inside a commercial story - successive discounts, instalment schemes, or growth of a deposit - and the marks hinge on choosing the right base and the right formula.
Core rules
- Ratio a : b with proportion a : b :: c : d means ad = bc; in a continued proportion the mean proportional b satisfies b² = ac.
- Successive percentage changes multiply, never add: overall multiplier = (1 + r₁)(1 + r₂)…
- SI = PRT/100; CI = P(1 + i)ⁿ − P, halving i and doubling n for half-yearly compounding.
- Present value of an annuity of ₹1 for n periods = [1 − (1 + i)⁻ⁿ]/i.
- nPr = n!/(n − r)! when order matters; nCr = n!/[r!(n − r)!] when it does not.
- AP: nth term a + (n − 1)d, sum = (n/2)[2a + (n − 1)d].
Worked example
A ₹5,000 article carries two successive discounts of 20% and 10%. A common answer of 30% gives ₹3,500, which is wrong. Multipliers give 5000 × 0.80 × 0.90 = ₹3,600, so the true discount is ₹1,400, i.e. 28%. The second discount is charged on the reduced price (₹4,000), not on ₹5,000.
Traps
Adding successive percentages; applying compounding to a simple-interest question; forgetting that the base changes after the first discount; and using nPr where the arrangement is unordered (a committee, not a queue).