How to Use / उपयोग कैसे करें

इसे exam से पहले last moment पर पढ़ने के लिए बनाया गया है — हर topic के सिर्फ most important formulas। Detailed explanation के लिए chapter wise files already हैं।

1️⃣ Percentage / प्रतिशत

• Percentage = (Value / Total) × 100
• Value = (Percentage × Total) / 100
• % Increase = (Increase / Original) × 100
• % Decrease = (Decrease / Original) × 100
• Final = Initial × (1 ± x/100)

2️⃣ Profit & Loss / लाभ और हानि

• Profit = SP − CP
• Loss = CP − SP
• Profit% = (Profit / CP) × 100
• Loss% = (Loss / CP) × 100
• SP = CP × (1 + P/100)
• SP = CP × (1 − L/100)
• CP = SP / (1 + P/100) या SP / (1 − L/100)

3️⃣ Discount / छूट

• Discount = MP − SP
• Discount% = (Discount / MP) × 100
• SP = MP × (100 − D)% / 100
• Successive discount: F = A + B − (A×B)/100

4️⃣ Simple & Compound Interest / साधारण व चक्रवृद्धि ब्याज

• SI = (P × R × T) / 100
• Amount (SI) = P + SI
• Amount (CI, annual) = P(1 + R/100)^T
• CI = Amount − P
• Difference (CI − SI, 2 yrs) = P×R² / 10000

5️⃣ Ratio, Proportion & Average / अनुपात व औसत

• a : b = a/b
• In proportion: a:b = c:d ⇒ ad = bc
• Average = Sum / Number of terms
• Total = Average × Number
• Share in ratio: प्रत्येक हिस्सा = (व्यक्तिगत भाग / कुल भाग) × Total

6️⃣ Time & Work / समय व कार्य

• If A completes in a days → 1 day work = 1/a
• A & B together: 1/a + 1/b
• Work = Time × Efficiency
• Time ∝ 1 / No. of workers
• Shortcut: LCM of days = total work units

7️⃣ Time, Speed & Distance / समय, गति व दूरी

• Distance = Speed × Time
• Speed = Distance / Time
• Time = Distance / Speed
• 1 km/hr = 5/18 m/s
• 1 m/s = 18/5 km/hr
• Relative speed (same dir) = A − B
• Relative speed (opp dir) = A + B

8️⃣ Mensuration 2D / क्षेत्रमिति 2D

• Square: Area = a², Perimeter = 4a
• Rectangle: Area = L×B, Perimeter = 2(L+B)
• Triangle: Area = ½×base×height
• Circle: Area = πr², Circumference = 2πr
• Parallelogram: Area = base×height
• Trapezium: Area = ½(a + b)h

9️⃣ Mensuration 3D / क्षेत्रमिति 3D

• Cuboid: TSA = 2(lb+bh+lh), Volume = lbh
• Cube: TSA = 6a², Volume = a³
• Cylinder: CSA = 2πrh, TSA = 2πr(r+h), V = πr²h
• Cone: CSA = πrl, TSA = πr(r+l), V = ⅓πr²h
• Sphere: TSA = 4πr², V = 4/3 πr³
• Hemisphere: CSA = 2πr², TSA = 3πr²

🔟 Number System, LCM & HCF / संख्याएँ

• Even = 2k, Odd = 2k+1
• LCM = product of highest powers of all primes
• HCF = product of lowest powers of common primes
• Divisibility: 2 → last digit even, 3/9 → sum of digits, 5 → last digit 0 or 5, 11 → (odd−even digits) multiple of 11

Note: Detailed explanation, examples & MCQ practice के लिए chapter-wise files use करें। यह page सिर्फ तेज़ revision के लिए है।