Quantitative Aptitude – Caselets
(Arunachal Pradesh TET – Teacher Eligibility Test)
Caselets are short, real‑life scenario problems that test your ability to apply basic math concepts (ratios, percentages, time–distance, profit‑loss, mixture, interest, etc.) in a narrative form.
They resemble a “mini‑story” with numbers that you must interpret, set up equations, and solve.
1. Simple Explanation
| What | How it works |
|---|---|
| Narrative | A paragraph (≈ 50–70 words) describing a situation (e.g., a shop’s sale, a train journey, a teacher’s salary). |
| Goal | Find the unknown quantity (price, time, profit, etc.). |
| Skills tested | • Reading comprehension • Extraction of key data • Translating words into mathematical expressions • Basic algebra/arithmetics |
Tip: Treat a caselet like a mini‑story; the answer is the “puzzle‑piece” that completes the picture.
2. Key Points to Remember
| # | Concept | What to Look For | Quick Note |
|---|---|---|---|
| 1 | Ratios & Proportions | “in a ratio of 3:4, the second quantity is 48” | Use (x/48 = 3/4) → (x = 36) |
| 2 | Percentages | “increased by 20 %”, “discount of 15 %”, “10 % of X” | Convert % to decimal: 20 % = 0.20 |
| 3 | Time–Distance | “travels 60 km in 2 h”, “two trains meet after 5 h” | Speed = Distance ÷ Time |
| 4 | Profit & Loss | “sold at 12 % profit”, “loss of ₹200 on ₹800” | Profit/Loss = (Selling – Cost) |
| 5 | Simple & Compound Interest | “simple interest of ₹120 on ₹1200 for 2 yrs” | SI = P × R × T / 100 |
| 6 | Mixture Problems | “mix 3 L of A (₹5/L) with 2 L of B (₹8/L)” | Weighted average: ( (3·5 + 2·8)/(3+2) ) |
| 7 | Work & Time | “two workers finish in 8 h, one in 12 h” | Work = 1/T; combine rates |
| 8 | Algebraic Equations | “if X is 5 more than Y, and X + Y = 20” | Set up: (X = Y + 5); solve |
| 9 | Unit Conversions | “400 m in 10 min” | 1 km = 1000 m, 1 h = 60 min |
| 10 | Checking Consistency | “if answer > 1000 but story says small” | Verify by back‑substitution |
General Approach
- Read once – highlight numbers, units, and what is asked.
- Write the given information in a list or a concise sentence.
- Translate words into equations (use variables if needed).
- Solve algebraically (or do a quick mental calculation if possible).
- Check the answer against the context.
3. Worked Example
Caselet:
“A teacher’s monthly salary is increased by 12 % after a merit award. If the new salary is ₹12 600, what was the original salary?”
Step‑by‑Step Solution
-
Identify the facts
- Increase = 12 %
- New salary = ₹12 600
-
Translate into an equation
Let original salary = (S).
After a 12 % increase:
[ S + 0.12S = 1.12S = 12,600 ] -
Solve for (S)
[ S = \frac{12,600}{1.12} = 11,250 ] -
Check
12 % of 11 250 = 1 350;
11 250 + 1 350 = 12 600 → ✔️
Final Answer
The original monthly salary was ₹11 250.
4. Quick Revision Summary
| Topic | Typical Question Type | Quick Formula |
|---|---|---|
| Ratios | “A:B = 3:5, B = 50” | (A = \frac{3}{5}B) |
| Percentages | “Discount 15 % on ₹200” | ( \text{Discount}=0.15×200=30) |
| Time–Distance | “Speed 60 km/h, time 2 h” | (D = V×T = 120) |
| Profit/Loss | “Sold for ₹180, cost ₹150” | (Profit = 30) |
| Simple Interest | “₹1 000 at 5 % for 3 yrs” | (SI = 1000×5×3/100 = 150) |
| Mixture | “3 L at ₹4/L + 2 L at ₹6/L” | (Avg = (3·4 + 2·6)/5 = 4.8) |
| Work | “X takes 8 h, Y 12 h” | Work rate (=1/T); combine |
| Algebra | “X = Y + 7, X+Y = 30” | Solve linear |