Ratio and percentage questions look easy — but they hide common traps. Use this checklist to protect your marks.
Mistake 1: Not simplifying the ratio first
Always simplify before you calculate. Example: $12:18 \to 2:3$.
Mistake 2: Mixing ratio and fraction language
If a part is “$2$ of $5$,” that is $\frac{2}{5}$ of the total. Make the fraction explicit before calculating.
Mistake 3: Percentage of a percentage
When a value changes by a percent, apply the change to the current value, not the original.
Mistake 4: Reverse percentage problems
If something is “after” a change, you need to divide by the multiplier. Example: A sale price of $$56$ after a $20\%$ discount → $56 \div 0.8 = $70$ original price.
Common wrong answer: $56 + 20\% \text{ of } 56 = 67.20$ — this is wrong because $20\%$ should be of the original, not the sale price.
Mistake 5: Sharing in a ratio — forgetting to find total parts
Example: Share $$240$ in the ratio $3:5$. Total parts: $3 + 5 = 8$. One part: $240 \div 8 = 30$. Shares: $$90$ and $$150$.
Quick Reference: Percentage Multipliers
| Change | Multiplier |
|---|---|
| Increase by $15\%$ | $\times 1.15$ |
| Decrease by $25\%$ | $\times 0.75$ |
| Find original after $20\%$ increase | $\div 1.20$ |
| Find original after $30\%$ decrease | $\div 0.70$ |
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