Commercial Mathematics

Bihar STET Paper 1: Commercial Mathematics (व्यवसायिक गणित)

Complete Revision Notes & PYQ Tricks (Stocks, Shares, Discount, CI/SI & Partnership)

Target: 12–15 Marks Hinglish Short Tricks Blogger Ready

1. Stocks & Shares (शेयर और लाभांश) - 5 Core Types

Face Value (FV / अंकित मूल्य): Company ka fixed print rate (Hamesha ₹10 ya ₹100 hota hai). Company isi par dividend deti hai.

Market Value (MV / बाजार मूल्य): Khareed ya bech keemat (Jeb se laga paisa). Investor ka actual profit return isi par check hota hai.

Dividend (लाभांश %): Har saal milne wali kamai. Rule: Dividend = Rate% × Face Value

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

[Type 1 PYQ] Equal Dividend & Ratio of Investment

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, find the ratio of investment in both stocks.

⚡ 5-Second Exam Hack:
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
✔ Answer: 16 : 15

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

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

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

[Type 3 PYQ] Annual Income from Investment

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

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

2. Successive Discounts (क्रमिक बट्टा / समतुल्य छूट)

• 2 Discounts (x% and y%): Net Discount = [x + y - (x × y / 100)]%
• 3 Discounts (x%, y%, z%): 100 maan kar sequential reduce karo!

[PYQ Example] 20% aur 10% ka Samtuly Batta:

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

3. CI vs SI Difference Formulas (2 & 3 Years)

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

[PYQ Example] 2-Year Difference = ₹15, Rate = 5%, Find Sum (P):

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

4. Partnership & Loan Installments

Partnership Rule: Profit Ratio = (Capital 1 × Time 1) : (Capital 2 × Time 2)

Equal Installment (CI): P = [x / (1 + R/100)] + [x / (1 + R/100)²]

⚡ Shortcut: Equal annual installment hamesha (100 + R) ke square ka multiple hoti hai!

[PYQ Example] Partnership Profit Share:

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
✔ Answer: ₹1600