BIHAR STET PAPER 1: COMPLETE COMMERCIAL MATHEMATICS

Bihar STET Paper 1 - Commercial Mathematics

Complete Visual Revision Notes & All PYQ Short Tricks (Pages 84–126)

Target: 12–15 Marks All 4 Core Topics Included 100% Error-Free Formatting

Topic 1: Stocks & Shares (शेयर और लाभांश)

5 PYQ Types

1. Face Value (FV / अंकित मूल्य)

Company ka fixed print price (Hamesha ₹10 ya ₹100). Company hamesha ispar dividend deti hai.

2. Market Value (MV / बाजार मूल्य)

Khareed ya bech keemat (Jeb se laga paisa). Investor ka munafa (Yield %) ispar nikalta hai.

3. Dividend Rate (लाभांश %)

Har saal milne wali kamai.
Dividend = Rate% × Face Value

Master Formulas:
• Number of Shares = Total Investment / Market Value (MV)
• Annual Income = Number of Shares × (Dividend Rate% × FV)
• Rate of Return (Yield %) = (Dividend per Share / Market Value) × 100
• Purchase Price (MV) = (Face Value × Dividend %) / Yield %

[PYQ Type 1] Equal Dividend & Investment Ratio (04 Sept 2023, Shift-II)

Question: Ramesh invests a part of money in 9% stock at ₹96 and remaining in 12% stock at ₹120. If annual dividend from both stocks is equal, what is the ratio of investment in both stocks?

⚡ 5-Second Direct Exam Trick:
Inv 1 / Inv 2 = (Price 1 / Rate 1) × (Rate 2 / Price 2)
Inv 1 / Inv 2 = (96 / 9) × (12 / 120)
= (32 / 3) × (1 / 10) = 32 / 30 = 16 : 15
✔ Correct Answer: 16 : 15

[PYQ Type 2] Purchase Price (MV) Given Yield %

Question: A person bought ₹25 shares from a company paying 9% dividend. If he gets 10% return on his investment, at what price did he buy?

Solution:
MV = (Face Value × Dividend %) / Yield %
MV = (25 × 9) / 10 = 225 / 10 = ₹22.50
✔ Correct Answer: ₹22.50

[PYQ Type 3] Total Annual Income from Investment

Question: A man invests ₹4455 in ₹10 shares quoted at ₹8.25. If dividend is 12%, find his total annual income.

Solution:
1. No. of Shares = 4455 / 8.25 = 540 shares
2. Dividend per share = 12% of ₹10 = ₹1.20
3. Total Annual Income = 540 × 1.20 = ₹648
✔ Correct Answer: ₹648

Topic 2: Successive Discounts (क्रमिक बट्टा / समतुल्य छूट)

High Frequency

Core Formulas:
• 2 Discounts (x% and y%): Net Discount = [x + y - (x × y / 100)]%
• 3 Discounts (x%, y%, z%): Initial 100 maan kar step-by-step minus karo.

[PYQ Pattern 1] 2 Successive Discounts

Question: Find the single discount equivalent to two successive discounts of 20% and 10%.

Net Discount = 20 + 10 - (20 × 10 / 100)
= 30 - 2 = 28%
✔ Correct Answer: 28%

[PYQ Pattern 2] 3 Successive Discounts (100 Method)

Question: A shopkeeper offers three successive discounts of 10%, 20%, and 25%. What is the net equivalent discount percentage?

1. Initial MP = 100
2. After 10% discount = 100 - 10 = 90
3. After 20% discount on 90 = 90 - 18 = 72
4. After 25% discount on 72 = 72 - 18 = 54
Net Discount = 100 - 54 = 46%
✔ Correct Answer: 46%

Topic 3: CI vs SI Difference Formulas (D2 & D3)

Direct Formulas

Master Formulas:
• Difference for 2 Years (D2) = P × (R / 100)²
• Difference for 3 Years (D3) = P × (R / 100)² × [(300 + R) / 100] = D2 × [(300 + R) / 100]

[PYQ Pattern 1] Find Principal (P) from 2-Year Difference

Question: The difference between CI and SI on a certain sum for 2 years at 5% per annum is ₹15. Find the principal sum.

15 = P × (5 / 100)²
15 = P × (1 / 20)² = P / 400
P = 15 × 400 = ₹6000
✔ Correct Answer: ₹6000

[PYQ Pattern 2] 3-Year Difference

Question: Find the difference between CI and SI on ₹1000 for 3 years at 10% per annum.

D3 = 1000 × (10 / 100)² × [(300 + 10) / 100]
D3 = 1000 × (1 / 100) × (310 / 100) = 10 × 3.1 = ₹31
✔ Correct Answer: ₹31

Topic 4: Partnership & Loan Installments (साझेदारी एवं किस्त)

Calculation Saver

Core Rules:
• Partnership: Profit Ratio = (Capital 1 × Time 1) : (Capital 2 × Time 2)
• 2 Equal Installments (CI): P = [x / (1 + R/100)] + [x / (1 + R/100)²]
⚡ Option Elimination Hack: Equal annual installment hamesha (100 + R) ke square ka multiple hoti hai!

[PYQ Pattern 1] Partnership Profit Share

Question: A invests ₹12000 for 8 months and B invests ₹16000 for 6 months. Total profit is ₹3200. Find A's share.

Profit Ratio = (12000 × 8) : (16000 × 6)
= 96000 : 96000 = 1 : 1
A's share = 3200 / 2 = ₹1600
✔ Correct Answer: ₹1600

[PYQ Pattern 2] Loan Equal Annual Installments

Question: A loan of ₹2100 is repaid in 2 equal annual installments at 10% p.a. compound interest. Find each installment.

2100 = [x / (11/10)] + [x / (121/100)]
2100 = (10x / 11) + (100x / 121) = 210x / 121
x = (2100 × 121) / 210 = 10 × 121 = ₹1210
✔ Correct Answer: ₹1210