Study Notes – Caselets (Quantitative Aptitude)
Target Exam: Goa Police Sub‑Inspector (SI) – Quantitative Aptitude
Exam Style: Short, self‑contained problems (Caselets) that test quick reasoning, numerical fluency, and application of basic formulas.
Tip:
Always read the problem carefully.
Identify the key requirement (number, ratio, difference, percentage, etc.).
Translate the word problem into a simple algebraic or arithmetic expression.
1. What Is a “Caselet”?
| Feature | Explanation |
|---|---|
| Definition | A concise, real‑world problem that can be solved in 1–3 minutes. |
| Structure | 1. Scenario (context) 2. Numerical data 3. Question (usually a single numeric answer). |
| Common Types | - Ratios & Proportions - Percentages & Growth - Time–Distance–Speed - Work & Wages - Simple Interest & Compound Interest - Age & Time - Probability (often omitted) - Miscellaneous (e.g., “If 3 men finish a job in 12 days, how many men will finish it in 8 days?”). |
2. Core Formulae & Quick‑Recall Tricks
| Category | Formula | Quick‑Recall Trick |
|---|---|---|
| Ratio / Proportion | ( \frac{a}{b} = \frac{c}{d} \Rightarrow ad = bc ) | “Cross‑multiply” – works for any two ratios. |
| Percentage | ( \text{Value} = \frac{\text{Percentage}}{100} \times \text{Total} ) | Think “per hundred” – replace “percent” with “/100”. |
| Growth / Decay | ( P_n = P_0(1 + r)^n ) (Compound) ( P_n = P_0(1 + rn) ) (Simple) |
Use “*1 + r” for compound; “*1 + rn” for simple. |
| Time–Distance–Speed | ( \text{Speed} = \frac{\text{Distance}}{\text{Time}} ) ( \text{Distance} = \text{Speed} \times \text{Time} ) ( \text{Time} = \frac{\text{Distance}}{\text{Speed}} ) |
Convert all units to the same system (km, h, m). |
| Work (Man‑Hours) | ( \text{Work} = \text{Rate} \times \text{Time} ) ( \frac{R_1}{R_2} = \frac{T_2}{T_1} ) (when same work) |
“Work done” = “rate × time.” |
| Simple Interest | ( SI = \frac{P \times R \times T}{100} ) | “P‑R‑T‑100” mnemonic. |
| Compound Interest (annual) | ( A = P(1 + \frac{R}{100})^T ) | “P times (1 + r/100)^T”. |
| Age Problems | Use algebraic substitution: ( x ) years ago, ( x ) years later. | “Let present age = (x)”; then formulate past/future expressions. |
3. Problem‑Solving Strategy (The 4‑Step Method)
-
Read & Understand
- Identify the objective (e.g., find speed, find percent).
- Note all given numbers and units.
-
Translate to Math
- Write the relevant formula(s).
- Substitute the numbers.
- If necessary, set up an algebraic equation.
-
Solve Quickly
- Use mental math tricks:
- Multiplication: ( 25 \times 4 = 100) → multiply by 100 and adjust.
- Division: ( 100 ÷ 4 = 25) → divide by 4 first then adjust.
- Percent: ( 30% \text{ of } 200 = 0.30 \times 200 = 60).
- Round intermediates only when the final answer is required to an integer; otherwise keep exact fractions.
- Use mental math tricks:
-
Check & Convert Units
- Verify that the answer unit matches the question.
- If the answer has a decimal, see if it can be converted to a fraction or percentage for clarity.
4. Common Tricky Points & Pitfalls
| Pitfall | Why It Happens | How to Avoid |
|---|---|---|
| Unit mismatch | Mixing km/h with m/min, or days with hours. | Convert all quantities to a common system before plugging into formulas. |
| Misreading “less” vs “more” | “Less than” vs “more than” in age problems. | Re‑write the sentence: “X is 5 years more than Y” → (X = Y + 5). |
| Assuming integer results | Some caselets yield fractional answers. | Keep fractions or decimals until the last step; only round if instructed. |
| Over‑complicating | Adding unnecessary variables. | Stick to the simplest variable, usually “x” for the unknown. |
| Neglecting “time” part | In speed problems, forgetting to convert 30 min to 0.5 h. | Always convert minutes to hours (or vice‑versa) by dividing/multiplying by 60. |
| Compound vs Simple interest confusion | Using simple formula for a compound scenario. | Check the problem statement for “compounded yearly/annually” or “simple interest”. |
5. Sample Problem with Step‑by‑Step Solution
Question:
A police convoy travels from City A to City B, a distance of 120 km.
The convoy starts at 08:00 AM, travels at a constant speed for the first 60 km, then reduces its speed by 25 km/h for the remaining distance.
If the convoy reaches City B