Arithmetic: interest, partnership and proportion
Arithmetic (WBBSE Madhyamik)
Arithmetic in the Madhyamik paper is applied commercial mathematics: simple and compound interest, partnership business, and ratio–proportion problems. Answers need correct units (₹, months, years) and a short statement of what has been found, not just a bare number.
Core rules
- Simple interest: I = Prt/100, and amount A = P + I.
- Compound interest: A = P(1 + r/100)^n, CI = A − P. For half-yearly compounding, halve r and double n; for quarterly, quarter r and quadruple n.
- For two years at the same rate, CI − SI = P(r/100)².
- Partnership: profit is shared in the ratio of capital × time, not capital alone.
- Proportion: a : b = c : d means ad = bc; in continued proportion b² = ac. In inverse proportion the product xy stays constant.
Worked example
₹8,000 at 10% per annum compounded half-yearly for 1 year. Half-yearly rate = 5%, number of periods = 2, so A = 8000(1.05)² = 8000 × 1.1025 = ₹8,820, and CI = ₹820. Annual compounding would have given ₹800; the extra ₹20 is interest earned on the first half-year's interest.
Traps
- Halving the rate but forgetting to double the time, or the reverse.
- Using the simple-interest formula when interest is reinvested each period.
- Dividing partnership profit by capital only, ignoring the months each partner stayed in the business.
- In proportion sums, inverting one ratio but not the other, which destroys the equality.
- Rounding a rate like 12.5% to 13% before substituting, then losing the exact answer.