These questions mix formulas with reasoning. The fastest candidates choose the correct model before calculating: cost-selling, work-rate, distance-speed-time, odd days or sufficiency.
Core Definitions
Data sufficiency
Standard definition: A question type where you decide whether given statements provide enough information to answer, without necessarily solving fully.
Exam meaning: पूरै solve नगरी statement पर्याप्त छ कि छैन भनेर निर्णय गर्ने question।
Work rate
Standard definition: Amount of work completed per unit time.
Exam meaning: एक unit time मा सकिने कामको भाग।
How To Think
Treat profit as price relation, work as rate addition, speed as distance/time, and calendar as odd-day counting. Data sufficiency requires independence testing of each statement.
Commercial and Rate Formulas
Know the formula and what each variable means.
| Topic | Formula | Meaning |
|---|---|---|
| Profit | SP – CP | Selling price minus cost price |
| Loss | CP – SP | Cost price minus selling price |
| Simple interest | P*T*R/100 | Principal-time-rate |
| Work | Rate = 1/time | Combine rates |
| Speed | Distance/time | Unit consistency |
Calendar and Sufficiency
Calendar problems use remainders; sufficiency uses logical completeness.
- Odd days are remainder days after complete weeks.
- Leap year has 366 days and 2 odd days; ordinary year has 1 odd day.
- Century leap rules need divisibility by 400.
- In data sufficiency, test statement I alone, II alone, then together.
- Do not solve more than needed.
Formulas and Rules
- Profit % = profit / CP x 100.
- Loss % = loss / CP x 100.
- Simple interest = PRT/100.
- If A finishes work in x days, A rate = 1/x per day.
- Distance = speed x time.
- Ordinary year odd days = 1; leap year odd days = 2.
Step-by-Step Method
- Identify variable and formula family.
- Check units before calculation.
- For work, convert days into rates.
- For calendar, count odd days and take mod 7.
- For data sufficiency, avoid using outside assumptions.
Worked Examples
- CP=100, SP=120 gives profit 20 and profit percent 20%.
- A does work in 10 days and B in 15 days. Combined rate = 1/10 + 1/15 = 1/6, so together 6 days.
- In sufficiency, if statement I gives exact age and II only gives relation, I alone may be sufficient.
| Area | Shortcut | Trap |
|---|---|---|
| Profit-loss | Percent on CP | Using SP as base |
| Work | Add rates | Adding days |
| Speed | Normalize units | Mixing km/h and m/s |
| Calendar | Use odd days | Forgetting leap year |
| Sufficiency | Test alone first | Solving with both too early |
Exam Point
- Profit/loss percentage is based on cost price.
- In work questions, never add times directly.
- Calendar answer depends on remainder after division by 7.
- Data sufficiency is about enough information, not final numeric answer.
Visual Practice
- Create CP-SP-profit triangle.
- Draw work-rate table.
- Make odd-day calendar chart.
- Use data sufficiency decision tree.
Common Mistakes
- Adding work days instead of rates.
- Ignoring unit conversion.
- Misapplying leap year rule.
- Combining statements before testing separately.
MCQ Revision
- Profit percent base?
- A 10-day worker rate?
- Leap year odd days?
- Simple interest formula?
- What does data sufficiency ask?
Final Summary
- Formula choice matters more than long calculation.
- Rate models solve work and speed.
- Calendar uses odd-day modular logic.
- Sufficiency tests information completeness.