Commercial Arithmetic and Elementary Statistics
This domain tests speed and accuracy in percentage, profit and loss, discount, interest and averages, plus computing and interpreting simple statistical measures.
Key formulae
- Profit% on cost = profit/CP × 100; SP = CP(100 + p)/100.
- Discount is calculated on marked price; successive discounts multiply: SP = MP(1 − d1)(1 − d2).
- SI = PRT/100; amount = P + SI.
- CI amount = P(1 + R/100)^n; for half-yearly use R/2 and 2n.
- Mean = sum of values ÷ number of values; median = middle value of ordered data; mode = most frequent value.
Worked example 1
Marked price ₹1,200 with successive discounts of 10% and 5%. SP = 1,200 × 0.90 × 0.95 = ₹1,026. A flat 15% would give ₹1,020 - successive discounts are never added.
Worked example 2
₹10,000 at 10% p.a. for 2 years compounded annually: amount = 10,000 × 1.10 × 1.10 = ₹12,100, so CI = ₹2,100. Simple interest for the same period is ₹2,000.
Presentation
Statistics questions also ask you to choose or read a bar diagram, histogram or pie chart, and to state which average suits which data. Mode suits shoe sizes; median suits data with extreme values.
Traps
Taking discount on cost price instead of marked price; adding successive discounts; not arranging data before finding the median; using months in place of years in PRT/100; rounding before the final step.