Basic Aptitude Formulas

1. Percentage Problem

Formula:

$$\text{Percentage} = \left(\frac{\text{Marks Obtained}}{\text{Total Marks}}\right) \times 100$$

---

2. Profit and Loss

Formula for Cost Price (when Selling Price and Profit Percentage are given):

$$\text{Cost Price} = \frac{\text{Selling Price}}{1 + \frac{\text{Profit Percentage}}{100}}$$

Formula for Profit Percentage (when Cost Price and Selling Price are given):

$$\text{Profit Percentage} = \left(\frac{\text{Selling Price} - \text{Cost Price}}{\text{Cost Price}}\right) \times 100$$

---

3. Simple Interest

Formula:

$$\text{Simple Interest} = \frac{P \times R \times T}{100}$$

Where:

• $P$ = Principal

• $R$ = Rate of Interest per annum

• $T$ = Time in years

---

4. Time and Work

Formula (If $W$ is work, $M$ is number of workers, and $T$ is time):

$$\text{Work Done} \propto \frac{1}{\text{Number of Workers}} \times \text{Time}$$

If $M_1$ workers take $T_1$ days, then $M_2$ workers will take:

$$\text{New Time} = \frac{M_1 \times T_1}{M_2}$$

---

5. Speed, Distance, and Time

Formula:

$$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$$

---

6. Age Problem

Formula:
If the sum of the ages of A and B is $S$, and A is $x$ years older than B, then:

$$\text{Age of A} = \frac{S + x}{2}, \quad \text{Age of B} = \frac{S - x}{2}$$

---

7. Number Series

The general formula for finding the next term in an arithmetic series is:

$$\text{Next Term} = \text{Last Term} + \text{Common Difference}$$

For geometric series, it's:

$$\text{Next Term} = \text{Last Term} \times \text{Common Ratio}$$

---

8. Ratio and Proportion

Formula:
If the ratio of A to B is $\frac{A}{B} = \frac{a}{b}$, then:

$$A = \frac{a}{b} \times B \quad \text{or} \quad B = \frac{b}{a} \times A$$

---

9. Average

Formula:

$$\text{Average} = \frac{\text{Sum of Numbers}}{\text{Total Numbers}}$$

---

10. Mixture Problem

Formula for Mixture Problems:

$$\frac{\text{Amount of Solute in First Mixture}}{\text{Total Volume}} = \frac{\text{Amount of Solute in Second Mixture}}{\text{New Total Volume}}$$

Or, more generally:

$$\frac{C_1 \times V_1 + C_2 \times V_2}{V_1 + V_2} = C_{\text{new}}$$

Where:

• $C_1, C_2$ = Concentrations of the first and second solutions

• $V_1, V_2$ = Volumes of the first and second solutions

• $C_{\text{new}}$ = New concentration after mixing

---