Fast Calculation for DI

At a glance 10 rules

1. 1Percentage change$\text{change}\ \% = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$$\text{index } 125 \to 150 \text{ is } \tfrac{25}{125} = 20\%,\ \text{not } 25\%$
2. 2Share of total$\text{share}\ \% = \dfrac{\text{part}}{\text{total}} \times 100$$\text{part} = \text{total} \times \dfrac{\text{share}}{100}$
3. 3Units and zerosSettle the units before dividing: 1 lakh is $10^5$, 1 crore is $10^7$, 1 tonne is 1,000 kg, and 'in thousands' adds three zeros.
4. 410% and 1% blocksFor a change, count 10% blocks of the old value in the difference, then 1% blocks: on a base of 640, a rise of 91 is $64 + 4 \times 6.4 + 1.4$, about 14.2%.
5. 5Round to two figuresRound each number to two significant figures (4,873 to 4,900) when the options are 5% or more apart; work exactly when two options are within 2%.
6. 6Compare two fractions$\dfrac{a}{b} > \dfrac{c}{d} \iff ad > bc$$\text{rate } k:\ \tfrac{a}{b} > k \iff a > kb$
7. 7Bridge close fractionsAdding the same number to top and bottom raises a fraction below 1. Adding $c$ to the top and $d$ to the bottom pulls $\tfrac{a}{b}$ towards $\tfrac{c}{d}$.
8. 8Reciprocals as percents

   $\tfrac{1}{7}$

   14.29%

   $\tfrac{1}{9}$

   11.11%

   $\tfrac{1}{11}$

   9.09%

   $\tfrac{1}{12}$

   8.33%

   $\tfrac{1}{13}$

   7.69%

   $\tfrac{1}{14}$

   7.14%

   $\tfrac{1}{15}$

   6.67%

   $\tfrac{1}{17}$

   5.88%

   $\tfrac{1}{18}$

   5.56%

   $\tfrac{1}{19}$

   5.26%

9. 9Product of two changes$\text{net}\ \% = p + q + \dfrac{pq}{100}$$p, q = \%\ \text{changes; a fall is negative}$
10. 10Ratio of two changes$\dfrac{A}{B}\ \text{moves by} \times \dfrac{100 + a}{100 + b}$$a, b = \%\ \text{changes in } A \text{ and } B$