Free preview · Lesson 1
Percentages and Profit & Loss
Percentage basics
A percentage is a fraction with denominator 100. Memorise these conversions, they save a lot of time:
- 1/2 = 50%, 1/3 = 33.33%, 1/4 = 25%, 1/5 = 20%, 1/6 = 16.67%
- 1/8 = 12.5%, 1/9 = 11.11%, 1/11 = 9.09%, 1/12 = 8.33%
x% of y = y% of x. So 16% of 25 = 25% of 16 = 4.
Successive change
If a value changes by a% and then by b%, the net change is a + b + ab/100 (use negative signs for decreases).
- Example: +20% then −20% gives 20 − 20 − 400/100 = −4%.
Keeping expenditure constant
If price rises by r%, consumption must fall by r/(100 + r) × 100%.
- Price up 25% → cut consumption by 25/125 = 20%.
Profit & Loss
- Profit = SP − CP; Profit % = Profit/CP × 100 (always on cost price).
- SP = CP × (100 + gain%)/100 and SP = CP × (100 − loss%)/100.
- Marked price with discount: SP = MP × (100 − d%)/100.
Worked example: Goods are marked 40% above cost and sold at 15% discount. SP = 1.40 × 0.85 = 1.19 × CP, so profit = 19%.
Two classic traps
- Two items sold at the same SP, one at x% gain and one at x% loss: there is always a loss of x²/100 %.
- A dishonest dealer using a 900 g weight for 1 kg gains (100/900) × 100 = 11.11%.