When profits and losses are applied one after another, we cannot simply add or subtract the percentages. Each percentage change acts on the new value, not the original price
If successive changes of a% and b% occur, the net effect formula is: Net% = a + b + (ab)/100. Use positive values for profit and negative values for loss. For three successive changes a%, b%, c%, first find net effect of any two, then apply the third change.
Questions typically involve 2-3 successive transactions. Common scenarios include buying-selling chains, discount followed by profit, or multiple markups. SSC often asks for overall profit/loss percentage or final selling price.
For quick calculation, convert percentages to multipliers. 20% profit = 1.2, 10% loss = 0.9. Multiply all factors: 1.2 × 0.9 = 1.08 = 8% overall profit.
Identify the changes First transaction: +20% (profit) Second transaction: -10% (loss)
Apply the formula Net% = a + b + (ab)/100 Net% = 20 + (-10) + (20 × (-10))/100 Net% = 20 - 10 - 200/100 Net% = 10 - 2 = 8%
Verify using multiplier method Final value = 1000 × 1.20 × 0.90 = 1000 × 1.08 = 1080 Profit = 1080 - 1000 = 80 Profit% = 80/1000 × 100 = 8% Answer: 8% overall profit Alternate Method using SP calculation: After first sale: 1000 × 120/100 = 1200 After second sale: 1200 × 90/100 = 1080 Net profit = 1080 - 1000 = 80 Profit% = 8%
Students often add percentages directly (20% - 10% = 10%) ignoring the compounding effect. Always remember that each subsequent percentage works on the changed value, not the original price. The interaction term (ab)/100 is crucial and frequently overlooked.
17graded MCQs · easy to hard · full solution & trap analysis