Mathematics
Mathematics in BSTC is arithmetic-dominant with a smaller algebra, geometry and mensuration component: number system, HCF–LCM, percentage, ratio and proportion, average, profit and loss, simple and compound interest, time–work, speed–distance, and area–volume formulae. Questions are short, so formula recall and clean calculation decide the score.
Core rules
- Percentage: successive changes multiply as factors (1.10 × 0.90), never add.
- Profit and loss: profit% is calculated on cost price; discount% is calculated on marked price.
- HCF–LCM: HCF × LCM = product of the two numbers (for two numbers).
- Average: sum ÷ count; adding a value changes the average by (new value − old average) ÷ new count.
- Interest: SI = PRT/100; CI = P(1 + r/100)^t − P.
- Time–work: add unit rates (1/a + 1/b), then invert; never average the days.
Worked example
A shopkeeper marks an article 40% above cost and then allows a 25% discount. What is the net result? Let CP = 100, so MP = 140. The discount is on the marked price: SP = 140 × 0.75 = 105. Profit = 105 − 100 = 5, so the profit is 5%. Note that adding 40% and subtracting 25% to get 15% is wrong, because the discount applies to the marked price, not to the cost price.
Traps that cost marks
Do not add successive percentage changes. Do not compute compound interest as simple interest for the second year. Check whether a mensuration question asks for curved surface area or total surface area, and keep units consistent before comparing. In ratio questions, convert all quantities to the same unit first.