{
  "quizTitle": "ICSE Class X - Commercial Mathematics (GST & Banking)",
  "quizCategory": "ICSE Class X",
  "quizSubject": "Mathematics",
  "questions": [
    {
      "id": 1,
      "section": "Section A: Theory & Concepts",
      "difficulty": "Easy",
      "questionText": "In an intra-state sale of goods, which two taxes are levied under GST?",
      "options": [
        "Only IGST",
        "CGST and SGST equally",
        "Customs Duty and SGST",
        "Cess and IGST"
      ],
      "correctOptionIndex": 1,
      "explanationText": "For intra-state transactions (within the same state), GST is shared equally between the Central Government (CGST) and State Government (SGST), each getting half of the total GST rate.",
      "hint": "The tax is split 50-50 between Central and State governments.",
      "derivationProof": "Statutory rule: Intra-state transaction occurs when Supplier location and Place of Supply are in the same state.\nTotal GST = Rate % × Value of supply.\nCentral Share: CGST = (Total GST / 2).\nState Share: SGST = (Total GST / 2)."
    },
    {
      "id": 2,
      "section": "Section A: Theory & Concepts",
      "difficulty": "Easy",
      "questionText": "If the rate of GST is 18%, what is the rate of CGST and SGST on an intra-state sale?",
      "options": [
        "18% CGST and 18% SGST",
        "9% CGST and 9% SGST",
        "12% CGST and 6% SGST",
        "18% IGST only"
      ],
      "correctOptionIndex": 1,
      "explanationText": "CGST rate = SGST rate = 18% / 2 = 9% each.",
      "hint": "Divide the 18% rate by two.",
      "derivationProof": "Given: GST Rate = 18%.\nIntra-state distribution formula:\nCGST Rate = GST Rate / 2 = 18% / 2 = 9%.\nSGST Rate = GST Rate / 2 = 18% / 2 = 9%."
    },
    {
      "id": 3,
      "section": "Section A: Theory & Concepts",
      "difficulty": "Board Standard",
      "questionText": "In a Recurring Deposit (RD) account, what is the formula for calculating total qualifying month-units (equivalent principal period in months) for n months?",
      "options": [
        "n(n - 1) / 2",
        "n(n + 1) / 2",
        "n² / 2",
        "2n + 1"
      ],
      "correctOptionIndex": 1,
      "explanationText": "The qualifying month-units are the sum of the first n natural numbers: 1 + 2 + ... + n = n(n + 1) / 2 months. To convert to years, divide by 12.",
      "hint": "Sum of first n natural numbers: n(n + 1)/2.",
      "derivationProof": "First deposit earns interest for n months.\nSecond deposit earns interest for (n - 1) months.\nLast deposit earns interest for 1 month.\nTotal equivalent period in months = n + (n - 1) + ... + 2 + 1.\nBy sum of A.P.: S = n(n + 1) / 2 month-units.\nDividing by 12 gives time in years: T = n(n + 1) / (2 × 12)."
    },
    {
      "id": 4,
      "section": "Section A: Theory & Concepts",
      "difficulty": "Easy",
      "questionText": "When is Integrated Goods and Services Tax (IGST) applicable?",
      "options": [
        "Only on intra-state sales within a Union Territory",
        "On inter-state sales across state borders and on imports",
        "Only on exports to neighboring countries",
        "On all local street vendor transactions"
      ],
      "correctOptionIndex": 1,
      "explanationText": "IGST is levied on all inter-state supplies of goods and/or services (sales from one state to another) as well as on imports into India.",
      "hint": "Applicable for movements crossing state boundaries.",
      "derivationProof": "Statutory rule: Inter-state transaction occurs when Supplier location and Place of Supply are in different states.\nUnder the IGST Act, the entire tax is levied as IGST by the Central Government, which is later apportioned to the consuming state."
    },
    {
      "id": 5,
      "section": "Section A: Theory & Concepts",
      "difficulty": "Board Standard",
      "questionText": "What is Input Tax Credit (ITC) under the GST system?",
      "options": [
        "A penalty imposed for delayed tax filing",
        "Credit claimed by a registered dealer for tax already paid on business purchases",
        "Discount given by a manufacturer directly to a retail consumer",
        "An extra tax paid on luxury goods"
      ],
      "correctOptionIndex": 1,
      "explanationText": "Input Tax Credit (ITC) allows registered businesses to deduct the tax already paid on raw material/inventory purchases (Input Tax) from the tax collected on sales (Output Tax).",
      "hint": "It prevents the cascading 'tax on tax' effect.",
      "derivationProof": "Net Tax Payable to Government = Output Tax (collected on sale) - Input Tax Credit (paid on purchase).\nITC = Tax paid on inward supplies."
    },
    {
      "id": 6,
      "section": "Section A: Theory & Concepts",
      "difficulty": "Board Standard",
      "questionText": "In a recurring deposit of monthly deposit P for n months at r% p.a., what is the total interest formula?",
      "options": [
        "I = P × [n(n + 1) / (2 × 12)] × (r / 100)",
        "I = P × n × (r / 100)",
        "I = P × [n(n - 1) / 12] × (r / 100)",
        "I = (P × n × r) / 24"
      ],
      "correctOptionIndex": 0,
      "explanationText": "Equivalent principal for 1 month = P × [n(n + 1) / 2]. Interest = (Equivalent Principal × r × 1) / (12 × 100) = P × [n(n + 1) / (2 × 12)] × (r / 100).",
      "hint": "Combine equivalent principal for 1 month with simple interest formula.",
      "derivationProof": "Equivalent principal for 1 month = P · [n(n + 1) / 2].\nTime period T = 1 month = 1 / 12 year.\nRate = r% per annum.\nInterest I = (Principal · Rate · Time) / 100\nI = (P · [n(n + 1) / 2] · r · 1) / (12 · 100)\nI = P · [n(n + 1) / 24] · (r / 100)."
    },
    {
      "id": 7,
      "section": "Section B: Application & Problem Solving",
      "difficulty": "Board Standard",
      "questionText": "A dealer in Delhi sells an article marked at ₹8,000 at a discount of 20% to a retailer in Mumbai. If the rate of GST is 12%, calculate the IGST paid by the retailer.",
      "options": [
        "₹768",
        "₹960",
        "₹384",
        "₹640"
      ],
      "correctOptionIndex": 0,
      "explanationText": "Selling price after 20% discount = 8,000 - 1,600 = ₹6,400. Since this is an inter-state sale (Delhi to Mumbai), IGST is charged: 12% of 6,400 = (12/100) × 6,400 = ₹768.",
      "hint": "GST is calculated on the discounted selling price (₹6,400), not the marked price.",
      "derivationProof": "Marked Price (MP) = ₹8,000.\nDiscount = 20% of ₹8,000 = (20/100) × 8,000 = ₹1,600.\nSelling Price (SP) = ₹8,000 - ₹1,600 = ₹6,400.\nTransaction is Inter-state (Delhi to Mumbai) ⇒ IGST applies.\nRate of IGST = 12%.\nIGST = 12% of ₹6,400 = (12/100) × 6,400 = ₹768."
    },
    {
      "id": 8,
      "section": "Section B: Application & Problem Solving",
      "difficulty": "Board Standard",
      "questionText": "A shopkeeper buys an article for ₹5,000 from a wholesaler within the same state and sells it to a consumer at ₹6,200. If the GST rate is 18%, what is the net GST paid by the shopkeeper to the State Government (SGST)?",
      "options": [
        "₹108",
        "₹216",
        "₹540",
        "₹936"
      ],
      "correctOptionIndex": 0,
      "explanationText": "Shopkeeper's profit/value addition = 6,200 - 5,000 = ₹1,200. Total GST payable = 18% of 1,200 = ₹216. Since tax is split equally, SGST paid = 216 / 2 = ₹108.",
      "hint": "Net tax payable by a dealer = Tax rate × Value Addition. SGST is half of that.",
      "derivationProof": "Purchase Price = ₹5,000; Selling Price = ₹6,200.\nInput Tax (SGST) paid on purchase = (9/100) × 5,000 = ₹450.\nOutput Tax (SGST) collected on sale = (9/100) × 6,200 = ₹558.\nNet SGST paid to State Govt = Output SGST - Input SGST\n= ₹558 - ₹450 = ₹108."
    },
    {
      "id": 9,
      "section": "Section B: Application & Problem Solving",
      "difficulty": "Board Standard",
      "questionText": "Kiran deposited ₹200 per month in a recurring deposit account for 36 months at 10% per annum. What is the maturity value Kiran receives?",
      "options": [
        "₹7,200",
        "₹8,310",
        "₹8,520",
        "₹9,000"
      ],
      "correctOptionIndex": 1,
      "explanationText": "Total deposit = 200 × 36 = ₹7,200. Qualifying month-units = 36 × 37 / 2 = 666. Interest = 200 × (666 / 12) × (10 / 100) = ₹1,110. Maturity value = 7,200 + 1,110 = ₹8,310.",
      "hint": "Principal deposited = 200 × 36 = 7,200. Interest = 200 × [36(37)/(2×12)] × (10/100) = 1,110.",
      "derivationProof": "P = ₹200, n = 36 months, r = 10% p.a.\nTotal sum deposited = P × n = 200 × 36 = ₹7,200.\nMonth-units = n(n + 1) / 2 = 36 × 37 / 2 = 18 × 37 = 666.\nInterest I = (P × Month-units × r) / (12 × 100)\nI = (200 × 666 × 10) / 1,200 = 133,200 / 120 = ₹1,110.\nMaturity Value (MV) = Total Deposit + Interest\nMV = ₹7,200 + ₹1,110 = ₹8,310."
    },
    {
      "id": 10,
      "section": "Section B: Application & Problem Solving",
      "difficulty": "Examiner Favorite",
      "questionText": "Mohan has a recurring deposit account in a bank for 2 years (24 months) at 6% p.a. If he gets ₹1,200 as interest at the time of maturity, find the monthly instalment.",
      "options": [
        "₹600",
        "₹750",
        "₹800",
        "₹1,000"
      ],
      "correctOptionIndex": 2,
      "explanationText": "I = P × [24 × 25 / (2 × 12)] × (6 / 100) ⇒ 1,200 = P × [600 / 24] × (6 / 100) ⇒ 1,200 = P × 25 × 0.06 ⇒ 1,200 = 1.5P ⇒ P = 1,200 / 1.5 = ₹800.",
      "hint": "Set up I = P × [n(n+1)/24] × (r/100) = 1,200 and solve for P.",
      "derivationProof": "Given: n = 2 years = 24 months, r = 6% p.a., I = ₹1,200.\nFormula: I = P · [n(n + 1) / 24] · (r / 100)\nSubstitute values:\n1,200 = P · [24 · 25 / 24] · (6 / 100)\n1,200 = P · 25 · 0.06\n1,200 = 1.5P\nP = 1,200 / 1.5 = ₹800.\nHence, monthly instalment is ₹800."
    },
    {
      "id": 11,
      "section": "Section B: Application & Problem Solving",
      "difficulty": "Examiner Favorite",
      "questionText": "A man invests ₹9,600 in shares of nominal value ₹100 each at a premium of ₹20. If the company declares an 8% dividend, calculate his annual income.",
      "options": [
        "₹640",
        "₹768",
        "₹800",
        "₹960"
      ],
      "correctOptionIndex": 0,
      "explanationText": "Market Value (MV) per share = 100 + 20 = ₹120. Number of shares = 9,600 / 120 = 80 shares. Nominal Value (NV) of 80 shares = 80 × 100 = ₹8,000. Annual dividend income = 8% of 8,000 = ₹640.",
      "hint": "Dividend is always calculated on the Nominal (Face) Value, never on Market Value.",
      "derivationProof": "Total Investment = ₹9,600.\nNominal Value (NV) per share = ₹100.\nPremium = ₹20 ⇒ Market Value (MV) per share = 100 + 20 = ₹120.\nStep 1: Number of shares = Investment / MV = 9,600 / 120 = 80 shares.\nStep 2: Total Face Value = 80 × ₹100 = ₹8,000.\nStep 3: Dividend % = 8%.\nAnnual Income = (8 / 100) × ₹8,000 = ₹640."
    },
    {
      "id": 12,
      "section": "Section B: Application & Problem Solving",
      "difficulty": "Examiner Favorite",
      "questionText": "What is the percentage return on the man's investment of ₹9,600 earning ₹640 annually?",
      "options": [
        "6.25%",
        "6.67%",
        "8.00%",
        "10.00%"
      ],
      "correctOptionIndex": 1,
      "explanationText": "Return % = (Annual Income / Total Investment) × 100 = (640 / 9,600) × 100 = 64 / 9.6 = 20 / 3% = 6.67% (6 2/3%).",
      "hint": "Return % = (Income / Investment) × 100.",
      "derivationProof": "Annual Income = ₹640.\nTotal Investment = ₹9,600.\nPercentage Return = (Annual Income / Total Investment) × 100%\n= (640 / 9,600) × 100%\n= (64 / 960) × 100%\n= (1 / 15) × 100% = 100 / 15% = 20 / 3% ≈ 6.67%."
    }
  ]
}