मात्रात्मक अभिरुचि (Quantitative Aptitude)
गणितीय अवधारणाहरूको व्यावहारिक प्रयोग परीक्षण गर्छ। शाखा अधिकृत परीक्षामा यो खण्डमा शीघ्र गणना र shortcut methods को महत्त्व छ।
1. Percentage (प्रतिशत)
मुख्य Formulas
| Concept | Formula |
|---|---|
| % of a number | x% of N = (x/100)×N |
| % increase | [(New−Old)/Old]×100 |
| % decrease | [(Old−New)/Old]×100 |
| A is what % of B | (A/B)×100 |
| Successive % | a+b+(ab/100) |
Fraction-Percent Conversion (याद गर्नुस्)
| Fraction | % | Fraction | % |
|---|---|---|---|
| 1/2 | 50% | 1/8 | 12.5% |
| 1/3 | 33.33% | 1/9 | 11.11% |
| 1/4 | 25% | 1/11 | 9.09% |
| 1/5 | 20% | 2/3 | 66.67% |
| 1/6 | 16.67% | 3/4 | 75% |
2. Ratio र Proportion (अनुपात)
Key Concepts
| Type | Formula | Example |
|---|---|---|
| Basic ratio | a:b = ka:kb | 2:3 = 4:6 |
| Compound ratio | (a:b)×(c:d) = ac:bd | 2:3 × 3:4 = 6:12 = 1:2 |
| Mean proportion | a:x = x:b → x=√(ab) | 4:x=x:9 → x=6 |
| Mixture rule (Alligation) | (Q1/Q2)=(C2−Mean)/(Mean−C1) | सस्तो-महँगो mix |
3. Simple र Compound Interest
Simple Interest (SI)
SI = PRT/100
Amount = P + SI
P = Principal, R = Rate%, T = Time(yr)
Compound Interest (CI)
A = P(1+R/100)ⁿ
CI = A − P
Half-yearly: R/2, n×2
Quarterly: R/4, n×4
4. Profit र Loss (नाफा-नोक्सान)
Formulas
| Concept | Formula |
|---|---|
| Profit % | [(SP−CP)/CP]×100 |
| Loss % | [(CP−SP)/CP]×100 |
| SP (given P%) | CP×(100+P%)/100 |
| CP (given SP, P%) | SP×100/(100+P%) |
| Dishonest dealer | Gain % = [Error/(True wt − Error)]×100 |
5. Time, Work र Pipes
Key Formulas
| Case | Formula |
|---|---|
| A ले n दिनमा काम गर्छ → 1 दिनको काम | 1/n |
| A र B मिलेर | 1/A + 1/B = 1/Total days |
| A ले n दिनमा भर्छ, B ले m दिनमा खाली गर्छ | Time = nm/(m−n) |
| Efficiency ratio a:b → Time ratio | b:a (inverse) |
6. Speed, Distance, Time
| Concept | Formula |
|---|---|
| Basic | Distance = Speed × Time |
| Average speed (same distance) | 2xy/(x+y) |
| Relative speed (same direction) | |S1−S2| |
| Relative speed (opposite) | S1+S2 |
| Train crossing pole | Time = Length/Speed |
| Train crossing platform | Time = (Train+Platform length)/Speed |
| km/hr → m/s | ×5/18 |
| m/s → km/hr | ×18/5 |
7. Mensuration (क्षेत्रमिति)
2D Shapes
| Shape | Area | Perimeter |
|---|---|---|
| Triangle | ½ × b × h | a+b+c |
| Rectangle | l × b | 2(l+b) |
| Square | a² | 4a |
| Circle | πr² | 2πr |
| Trapezium | ½(a+b)×h | — |
3D Shapes
| Shape | Volume | CSA |
|---|---|---|
| Cube | a³ | 4a² |
| Cuboid | lbh | 2h(l+b) |
| Cylinder | πr²h | 2πrh |
| Cone | ⅓πr²h | πrl |
| Sphere | 4/3πr³ | 4πr² |
• % succession: a+b+ab/100
• SI = PRT/100 | CI: A=P(1+r/n)^nt
• CI−SI (2yr) = P(R/100)²
• Profit/Loss % always on CP
• Avg speed (same dist) = 2xy/(x+y)
• km/hr × 5/18 = m/s
• Circle: Area=πr², Perimeter=2πr
• Cylinder Volume = πr²h
Q1. एउटा वस्तु Rs.800 मा किनेर Rs.1000 मा बेचियो। नाफा प्रतिशत?
(A) 20% (B) 25% (C) 30% (D) 15%
→ (B) 25% → (200/800)×100=25%
Q2. 60 km/hr को m/s मा रूपान्तरण?
(A) 16.67 m/s (B) 20 m/s (C) 18 m/s (D) 15 m/s
→ (A) 16.67 → 60×5/18 = 16.67
Q3. A ले 10 दिनमा र B ले 15 दिनमा काम गर्छ। दुवैले मिलेर कति दिनमा?
(A) 5 (B) 6 (C) 7 (D) 8
→ (B) 6 → LCM(10,15)=30; A=3/day, B=2/day; Total=5/day; Days=30/5=6