Elementary Arithmetic: Base, Rate and Units
What is tested
Arithmetic covers the number system, HCF–LCM, percentage, ratio, average, profit–loss, interest, time–work, speed–distance, mensuration and simplification. The paper rewards fast, exact calculation and unit discipline more than long derivations.
Core rules
- Percentage change is always on the original base; successive changes multiply, not add.
- Profit% = (SP − CP)/CP × 100; discount% is on marked price.
- SI = PRT/100; CI = P[(1+R/100)^T − 1].
- Work: take total work as the LCM of days; combine rates.
- Speed: convert km/h to m/s by ×5/18; average speed for equal distances is 2xy/(x+y).
- Mensuration: area of a circle πr², circumference 2πr; volume of a cylinder πr²h.
Worked example
A shopkeeper marks an item at ₹1,000 and gives discounts of 20% and 10%. First discount: 1,000 × 0.80 = ₹800. Second: 800 × 0.90 = ₹720. Total discount = ₹280, i.e. 28%. The single equivalent discount is 1 − (0.8 × 0.9) = 0.28, not 30%.
Traps
Do not add 20% and 10% to get 30%. In CI, interest earns interest-never use SI for more than one year unless asked. In time–work, if A is twice as efficient as B, A takes half the time, not double. Check whether a question asks for a ratio or a value before marking.