Commercial Arithmetic, Percentages and Interest

This topic covers money-related calculations frequently tested in word-problem form: percentages, profit/loss, discounts, and interest.

• Percentage: Means "per 100" — a way of expressing a number as a fraction of 100 (e.g., 25% = 25/100 = 1/4).
• Percent change formula:
• Percent change = (New value - Old value) / Old value x 100
• A positive result means a percentage increase; a negative result means a percentage decrease.
• Example: price rises from 200 to 250 → change = (250-200)/200 x 100 = 25% increase.
• Profit and loss:
• Profit = Selling Price (SP) - Cost Price (CP)
• Loss = Cost Price (CP) - Selling Price (SP)
• Both profit % and loss % are always calculated on the Cost Price, not the selling price.
• Example: CP=100, SP=120 → Profit=20, Profit% = 20/100 x 100 = 20%.
• Marked price and discount:
• Final price = Marked Price x (1 - discount/100)
• Example: Marked price 1000 with 20% discount → final price = 1000 x 0.8 = 800.
• Successive discounts:
• When multiple discounts are applied one after another, they multiply the remaining percentages — they do not simply add together.
• Example: successive discounts of 10% and 20% leave 90% x 80% = 72% of the original price — a combined discount of 28%, not 30%.
• Simple interest:
• Simple Interest (SI) = (P x r x t) / 100, where P = Principal (initial amount), r = rate of interest per year (%), t = time in years.
• Amount (A) = Principal (P) + Interest (I)
• Example: P=1000, r=5%, t=2 years → SI = (1000x5x2)/100 = 100; Amount = 1000+100 = 1100.

Test tip: Watch for questions combining successive discounts with profit/loss — always apply discounts first to find the final SP, then calculate profit or loss on the CP.