Quantitative Aptitude & Arithmetic for ADRE 2.0: Formulas & Shortcuts

The Mathematics paper in the Assam Direct Recruitment Examination consists of Class 10 SEBA standard arithmetic. Speed and accuracy under strict time limits determine your ranking.

1. Essential Formula Cheat Sheet

A. Percentage & Profit & Loss

• $\text{Percentage Increase/Decrease} = \frac{\text{Difference}}{\text{Original Value}} \times 100$
• $\text{Gain %} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100$
• $\text{Loss %} = \left( \frac{\text{Loss}}{\text{Cost Price}} \right) \times 100$
• $\text{Selling Price (SP)} = \text{CP} \times \left( \frac{100 + \text{Gain %}}{100} \right)$

B. Simple & Compound Interest

• Simple Interest (SI): $\text{SI} = \frac{P \times R \times T}{100}$
• Compound Interest (CI): $A = P \left(1 + \frac{R}{100}\right)^T$
• Difference between CI and SI for 2 Years: $\text{Difference} = P \left( \frac{R}{100} \right)^2$

C. Time, Work & Pipes

• If $A$ can do a job in $x$ days and $B$ in $y$ days, together they complete it in: $$\text{Combined Time} = \frac{x \times y}{x + y} \text{ days}$$
• Total Work is conventionally calculated as the LCM of the individual day counts.

2. Time-Saving Shortcut Tricks

1. Divisibility Rule of 11: Difference between the sum of digits in odd places and sum of digits in even places must be $0$ or divisible by $11$.
2. Successive Percentage Change: If a value changes by $+a%$ and then by $+b%$, net change is: $$\text{Net Change} = a + b + \frac{a \times b}{100}$$
3. Speed Conversion:
   • To convert $\text{km/h}$ to $\text{m/s}$, multiply by $\frac{5}{18}$.
   • To convert $\text{m/s}$ to $\text{km/h}$, multiply by $\frac{18}{5}$.