Percentage

Memorize these to avoid division during exams.

• 1/2 = 50%
• 1/3 = 33.33%
• 1/4 = 25%
• 1/5 = 20%
• 1/6 = 16.66%
• 1/7 = 14.28%
• 1/8 = 12.5%
• 1/9 = 11.11%
• 1/10 = 10%
• 1/11 = 09.09%
• 1/12 = 8.33%
• 1/15 = 6.66%
• 1/16 = 6.25%
• 3/8 = 37.5%, 5/8 = 62.5%

If $A \times B = Constant$, then if A increases by $x\%$, B must decrease by $y\%$.
Rule: If A increases by $1/n$, B must decrease by $1/(n+1)$ to keep product constant.

• Sugar Price Example: Price $\uparrow 25\% (1/4)$. Consumption must $\downarrow 1/(4+1) = 1/5 = 20\%$.

When a value changes by $x\%$ and then by $y\%$.

• Formula: Net Change = $x + y + \frac{xy}{100} \%$.
• Tip: Use this for Compound Interest (2 years) and Area questions (Length/Breadth change).
• For 3 Changes: Apply formula on first two, then result with third.

For continuous growth/depreciation.

• After n years: $P(1 \pm \frac{R}{100})^n$
• Short Trick: Use Ratio Method. If 10% increase (1/10), ratio moves $10 \to 11$. For 2 years, $10^2 \to 11^2$ i.e., $100 \to 121$.

Use for 'Both', 'Either', 'Neither' questions.

• Formula: $n(A \cup B) = n(A) + n(B) - n(A \cap B)$.
• Visualization: Draw two overlapping circles. Middle part is 'Both'. Total area must be 100% (or Total - None).

Core logic: Total Votes = Valid + Invalid. Winner - Loser = Majority.

• Valid Votes: Total - Invalid.
• Winner's Share: Usually % of Valid Votes (read carefully).

Passing Marks are constant.

• Concept: If Student A fails by $x$ marks and Student B passes by $y$ marks, difference in % = difference in marks ($x+y$).

Inverse relation between Net Income and Tax Rate.

• Rule: If Tax Rate increases by $R$ and Net Income decreases by $r$, then $Rate \times R = Net \times r$.
• Rate = $\frac{\text{Change in Net Income}}{\text{Total Income}} \times 100$.