Quantitative reasoning in objective paper must be fast and accurate. For engineers, the concepts are simple; the exam pressure is in arithmetic discipline and option elimination.
Core Definitions
Percentage
Standard definition: A fraction expressed per hundred.
Exam meaning: कुनै value लाई 100 को आधारमा व्यक्त गर्ने तरिका।
Ratio
Standard definition: A comparison of two or more quantities by division.
Exam meaning: दुई quantity बीचको तुलनात्मक सम्बन्ध।
How To Think
Use proportional thinking. Percent, fraction, ratio and average are different forms of the same idea: relation between quantities. Convert to the form that makes calculation easiest.
Fast Conversion
Common conversions reduce calculation time.
| Fraction | Percent | Decimal |
|---|---|---|
| 1/2 | 50% | 0.5 |
| 1/3 | 33.33% | 0.333 |
| 1/4 | 25% | 0.25 |
| 1/5 | 20% | 0.2 |
| 1/8 | 12.5% | 0.125 |
Average and Ratio Logic
Average is total per item; ratio is relative share.
- Average = sum / number of observations.
- Total = average x count.
- Weighted average depends on group size.
- Ratio a:b means total parts = a+b.
- If ratio and total are known, one part = total / total parts.
Formulas and Rules
- Percentage = part / whole x 100.
- Percentage increase = increase / original x 100.
- Average = sum / n.
- Arithmetic progression nth term = a + (n – 1)d.
- Sum of AP = n/2 [2a + (n – 1)d].
Step-by-Step Method
- Convert percentage to fraction when possible.
- For ratio, convert all quantities into parts.
- For average, find total first.
- For AP, identify first term and common difference.
- Estimate option range before exact calculation.
Worked Examples
- If 30% of 240 = 72, use 3/10 of 240.
- Ratio 2:3 with total 100 means one part 20, shares 40 and 60.
- Average of 10, 20, 30 is total 60/3 = 20.
| Question Type | Fast Start | Common Trap |
|---|---|---|
| Percent change | Use original as base | Using final as base |
| Ratio | Find one part | Adding actual values wrongly |
| Average | Convert to total | Averaging averages without weights |
| AP | Find d | Assuming multiplication series |
Exam Point
- Percentage base is always important.
- Weighted average is not simple average of averages.
- Ratio questions become easy after finding one part.
- Memorize common fraction-percent values.
Visual Practice
- Make percent-fraction chart.
- Draw ratio bar model.
- Use average-total-count triangle.
- Create AP term table.
Common Mistakes
- Taking percent of wrong base.
- Ignoring weight in average.
- Confusing ratio with difference.
- Calculation without approximation check.
MCQ Revision
- What is 1/8 as percent?
- Average formula?
- AP nth term?
- If ratio 3:2 total 50, what is one part?
- Percentage increase uses which base?
Final Summary
- Percent, ratio and average are proportional tools.
- Base quantity controls percentage.
- Total-first thinking solves averages.
- AP needs first term and common difference.