📚 Quantitative Aptitude – Caselets
(For the Chhattisgarh Police Constable Examination)
1️⃣ What are “Caselets”?
Caselets are short, real‑life word problems that test your ability to interpret data, set up equations, and solve for unknowns.
They are usually 3–5 sentences long and cover topics such as:
- Time & Motion
- Work & Rates
- Profit & Loss
- Interest (simple & compound)
- Mixture & Dilution
- Ratio & Proportion
- Percentage & Growth
- Basic Algebra (one‑step, two‑step, single‑variable equations)
The key to ace them is to read carefully, identify the given data, decide what you need to find, and apply the right formula.
2️⃣ Simple Explanation
| Step | Action | What to Look For |
|---|---|---|
| 1 | Read the whole problem twice | Hidden numbers, units, conditions |
| 2 | Identify variables | Assign letters to unknowns |
| 3 | Spot relationships | “In 6 days, X finished 3/4 of the job” → Rate = 3/4 ÷ 6 |
| 4 | Choose the formula | Work: Rate × Time = Work; Profit: Profit = (Selling Price – Cost) × Units |
| 5 | Set up the equation | Write it in standard algebraic form |
| 6 | Solve | Use substitution, elimination, or direct calculation |
| 7 | Check units & reasonableness | Hours, Days, Percentages should make sense |
3️⃣ Key Points to Remember
| # | Concept | Quick Tip |
|---|---|---|
| 1 | Unit Conversion | Convert everything to a common unit (e.g., all times to hours, all distances to km). |
| 2 | Rates & Work | Rate = Work ÷ Time. If two persons work together, add their rates. |
| 3 | Profit & Loss | Profit % = (Profit ÷ Cost) × 100. Loss % is similar with a minus sign. |
| 4 | Interest | Simple: I = P × R × T; Compound: A = P(1 + r/n)^(nt). |
| 5 | Mixtures | Use concentration × volume or mass × fraction. |
| 6 | Ratios | For A : B = m : n, A = m × k, B = n × k. |
| 7 | Percentage Changes | New Value = Old Value × (1 ± %/100). |
| 8 | Algebraic Manipulation | Keep equations balanced; always isolate the variable. |
| 9 | Check for “More than” / “Less than” | Often a trick: “more than 5 days” → 5 + x. |
| 10 | Logical Reasoning | Sometimes a problem gives a “contradiction” to spot; ignore impossible scenarios. |
4️⃣ Problem‑Solving Checklist
- Extract all numbers → list them.
- Define a variable for the unknown quantity.
- Choose the right formula from the table above.
- Write the equation.
- Solve, simplifying step‑by‑step.
- Round only when the question asks; otherwise keep exact values.
- Verify by plugging back into the original context.
5️⃣ Worked Example (Caselet)
Caselet:
“Two workers, A and B, can complete a road repair job in 12 and 18 days respectively when working alone. They start the job together but after 4 days B leaves and A continues alone. How many total days will the job take?”
Step‑by‑Step Solution
| Step | Explanation | Formula / Calculation |
|---|---|---|
| 1 | Find rates | A’s rate = 1 job / 12 days = 1/12 per day. B’s rate = 1 job / 18 days = 1/18 per day. |
| 2 | Combined rate for 4 days | Rate together = 1/12 + 1/18 = (3+2)/36 = 5/36 jobs per day. Work done in 4 days = (5/36) × 4 = 20/36 = 5/9 of the job. |
| 3 | Remaining work | 1 – 5/9 = 4/9 of the job left. |
| 4 | Time for A alone to finish | A’s rate = 1/12 job/day. Time = (4/9) ÷ (1/12) = 4/9 × 12 = 48/9 = 16/3 = 5.33 days. |
| 5 | Total time | 4 days (together) + 5.33 days (A alone) = 9.33 days ≈ 9 days 8 hours. |
Answer: The job will be finished in 9 days 8 hours (or 9.33 days).
6️⃣ Quick Revision Summary
- Read twice, note every number & unit.
- Define variables → keep them simple (
x,y). - Choose the right formula from the core topics.
- Set up the equation with correct units.
- Solve algebraically; double‑check with the original context.
- Remember common pitfalls:
- Mixing units (hours vs days).
- Forgetting to subtract work done already.
- Misreading “more than” or “less than”.
- Ign