Quantitative Aptitude – Caselets
Study Notes for Dadra & Nagar Haveli & Daman & Diu Police Constable Exam
1. Simple Explanation
A caselet is a short, real‑world problem that requires you to apply arithmetic, algebra, or basic geometry to find the answer.
Typical features:
| Feature | What to look for |
|---|---|
| Narrative | A brief story (e.g., two trains, a shop, a mixture). |
| Numbers | Usually 3–6 numerical values. |
| Question | A single question that can be answered with a single number or ratio. |
| Units | Often omitted (assume consistent units). |
Goal: Read once, extract the facts, set up a simple equation, solve, and check.
2. Key Points & Tricks
| Category | Tips |
|---|---|
| Reading | • Read the whole caselet once to grasp the context. • Highlight/underline all numbers and variables. |
| Identify Variables | • Assign a letter to each unknown (e.g., (x) = speed, (t) = time). |
| Choose a Strategy | • Ratio/Proportion – when “in proportion” or “in the ratio” is mentioned. • Percentage – for “increases by 20%” etc. • Work‑Time – “can complete a job in X days.” • Distance‑Time – “travels at Y km/h.” |
| Set Up Equation | • Translate the story into a mathematical relation. • Keep units consistent. |
| Solve | • Simplify step by step. • Check for sanity (e.g., negative times? impossible speeds?). |
| Answer Format | • If asked for a ratio, give the simplest form. • If a number, round only if the question says “nearest integer.” |
| Time Management | • Allocate 2–3 minutes per caselet; skip if stuck and return if time permits. |
3. Worked Example
Caselet
Two workers, A and B, start a road‑construction job at the same time. A can finish the job alone in 12 days, while B can finish it in 18 days. They work together for 5 days and then A stops working. How many more days will B need to finish the remaining work?
Step‑by‑Step Solution
-
Translate into rates
- A’s rate: ( \displaystyle \frac{1}{12}) of the job per day.
- B’s rate: ( \displaystyle \frac{1}{18}) of the job per day.
-
Work done together in 5 days
[ \text{Work}_{\text{both}} = 5 \left(\frac{1}{12} + \frac{1}{18}\right) = 5 \left(\frac{3+2}{36}\right) = 5 \left(\frac{5}{36}\right) = \frac{25}{36} ]
-
Remaining work
[ \text{Remaining} = 1 - \frac{25}{36} = \frac{11}{36} ]
-
Time B needs alone
[ \text{Time}_B = \frac{\text{Remaining}}{\text{Rate}_B} = \frac{\frac{11}{36}}{\frac{1}{18}} = \frac{11}{36} \times 18 = \frac{11}{2} = 5.5 \text{ days} ]
-
Answer
B will need 5.5 days (i.e., 5 days and 12 hours) to finish the job.
4. Quick Revision Summary
- Read Carefully – one pass to understand the context, then highlight numbers.
- Assign Variables – give each unknown a clear letter.
- Choose the Right Formula – ratio, percentage, work‑time, distance‑time, mixture, profit‑loss.
- Set Up the Equation – translate the story into a mathematical relationship.
- Solve Systematically – simplify, isolate the variable, compute.
- Check Reasonableness – ensure the answer makes sense (positive, realistic).
- Answer in Required Format – simplest form, nearest integer only if specified.
- Time Management – 2–3 min per caselet; move on if stuck, return if time allows.
Use these notes as a quick refresher before the exam and practice with at least 10–15 caselets to build speed and accuracy. Good luck!