General Mathematics
General Mathematics tests school-level arithmetic and mensuration applied quickly and accurately. High-yield areas: number system and HCF/LCM, percentage, profit and loss, simple and compound interest, ratio and proportion, average, time and work, time and distance, and the area and perimeter of standard figures.
Core rules
- Percentage change = (change ÷ original) × 100; always identify the base first.
- Profit% and loss% are calculated on cost price unless stated otherwise.
- Discount is always calculated on marked price.
- Simple interest = P × R × T / 100; compound amount = P(1 + R/100)^T.
- Work: if A finishes a job in x days, one day's work = 1/x; combined rate = 1/x + 1/y.
- Speed = distance ÷ time; convert km/h to m/s by multiplying by 5/18.
Worked example
A shopkeeper marks an article 40% above cost price and allows a 25% discount. Find his profit percent. Take CP = 100. Marked price = 100 × 1.40 = 140. Selling price = 140 × 0.75 = 105. Profit = 105 − 100 = 5 on a cost of 100, so profit = 5%. The 40% markup and 25% discount do not cancel because the discount applies to the larger marked price.
Traps that cost marks
- Applying the discount to cost price instead of marked price.
- Adding successive percentage changes directly (10% then 10% is 21%, not 20%).
- Mixing units: cm with m, minutes with hours.
- Treating average speed as the arithmetic mean; use total distance ÷ total time.
- Forgetting that compound interest earns interest on interest.