Question 1

To receive equal dividends from 9% stock at 96 and 12% stock at 120, in what ratio should the money be invested (9% at 96 : 12% at 120)?

Accepted Answer

Given data Stock A: 9 percent at 96 ⇒ dividend per rupee invested = 9/96 Stock B: 12 percent at 120 ⇒ dividend per rupee invested = 12/120 Equal total dividends from both portions. Concept / Approach Let investments be A and B. Equate A × (9/96) and B × (12/120) and solve A : B. Step-by-step calculation A × (9/96) = B × (12/120)A/B = (12/120) ÷ (9/96) = (1/10) ÷ (3/32) = (1/10) × (32/3) = 32/30 = 16/15Investment ratio (9% at 96 : 12% at 120) = 16 : 15 Verification Pick A = 16k, B = 15k. Dividends: 16k × 9/96 = 1.5k and 15k × 12/120 = 1.5k; equal as required. Common pitfalls Using face values rather than market prices when computing dividend per rupee invested. Inverting the ratio accidentally. Final Answer 16 : 15

Question 2

By investing Rs 1620 in 8 percent stock, the annual dividend is Rs 135. What is the market price (quotation) of the stock?

Accepted Answer

Given data Total investment = Rs 1620 Dividend received = Rs 135 per year Stock rate = 8 percent (Rs 8 per Rs 100 face) Concept / Approach Dividend yield on investment = Dividend / Investment. For a stock of 8 percent, market price M satisfies 8 / M = Dividend / Investment. Step-by-step calculation Dividend rate on investment = 135 / 1620 = 1/12 = 0.083338 / M = 1/12 ⇒ M = 8 × 12 = Rs 96 Verification At Rs 96 per Rs 100 face, Rs 1620 buys 1620/96 × 100 face = 1687.5 face; dividend = 0.08 × 1687.5 = 135. Common pitfalls Confusing face value with market value while equating yields. Using 8 percent of investment directly without the price adjustment. Final Answer Rs 96

Question 3

A 6 percent stock yields 8 percent. Find the market price of the stock.

Accepted Answer

Given data Coupon rate = 6 percent on Rs 100 face ⇒ dividend Rs 6 Investor yield required = 8 percent Concept / Approach Yield = Dividend / Market Price. Solve 8 percent = 6 / Price. Step-by-step calculation 6 / Price = 0.08 ⇒ Price = 6 / 0.08 = Rs 75 Verification At Rs 75, dividend 6 gives 6/75 = 0.08 = 8 percent. Common pitfalls Reversing the ratio as Price / Dividend. Applying the 8 percent to face value instead of market value. Final Answer Rs 75

Question 4

Sakshi invests part of Rs 12,000 in 12 percent stock at Rs 120 and the rest in 15 percent stock at Rs 125. If the total annual dividend is Rs 1,360, how much is invested in the 12 percent stock at Rs 120?

Accepted Answer

Given data Total capital = Rs 12,000 12 percent at Rs 120 ⇒ yield on investment = 12/120 = 10 percent 15 percent at Rs 125 ⇒ yield on investment = 15/125 = 12 percent Total dividend = Rs 1,360 Concept / Approach Let x be the rupees invested at 12 percent at Rs 120. Remaining is 12,000 − x invested at 15 percent at Rs 125. Dividend additivity: 0.10 x + 0.12 (12,000 − x) = 1,360. Step-by-step calculation 0.10x + 0.12(12,000 − x) = 1,3600.10x + 1,440 − 0.12x = 1,360−0.02x = −80 ⇒ x = Rs 4,000 Verification Dividend from Rs 4,000 at 10 percent = 400; from Rs 8,000 at 12 percent = 960; total = 1,360. Common pitfalls Using coupon rates directly on the face value portion rather than the market-based yields on invested rupees. Final Answer Rs 4,000

Question 5

By investing in 16⅔ percent stock at Rs 64, one earns Rs 1,500 per year in dividends. What is the investment amount?

Accepted Answer

Given data Coupon rate = 16⅔ percent = 50/3 per Rs 100 face Market price = Rs 64 per Rs 100 face Annual dividend received = Rs 1,500 Concept / Approach Dividend per rupee invested = (Dividend per 100 face) / Market price. Investment = Total dividend ÷ Dividend per rupee. Step-by-step calculation Dividend per rupee invested = (50/3) / 64 = 50/192 = 25/96Investment = 1,500 ÷ (25/96) = 1,500 × 96 / 25 = Rs 5,760 Verification At Rs 5,760 invested, face value bought = 5,760/64 × 100 = 9,000; dividend = 16⅔ percent of 9,000 = 1,500. Common pitfalls Multiplying by 64 instead of dividing when converting from face to market. Using 16⅔ percent of investment directly, which ignores the price premium or discount. Final Answer Rs 5,760

Question 6

Which is the better investment: 11 percent stock at 143 or 9¾ percent stock at 117?

Accepted Answer

Given data Choice A: 11 percent at 143 ⇒ yield = 11/143 Choice B: 9¾ percent at 117 ⇒ yield = 9.75/117 Concept / Approach Higher dividend per rupee invested implies better investment. Step-by-step calculation Yield A = 11/143 ≈ 0.07692 = 7.692 percentYield B = 9.75/117 = 0.083333... = 8.333 percentCompare: 8.333 percent > 7.692 percent ⇒ 9¾% stock at 117 is better Verification Both computations use dividend per Rs 100 face divided by market price, the standard convention. Common pitfalls Comparing coupon rates alone without adjusting for market price. Taking percentage of face value rather than price paid. Final Answer 9¾% stock at 117

Question 7

Find the cost price of a Rs 100 stock at 4 discount when brokerage is 1/4 percent.

Accepted Answer

Given data Quoted at 4 discount ⇒ market price = Rs 96 per Rs 100 face Brokerage = 0.25 percent on the market price Concept / Approach Total cost price = Market price + Brokerage. Brokerage is computed as a percentage of the amount paid to the market. Step-by-step calculation Market price = Rs 96Brokerage = 0.25 percent of 96 = 96 × 0.0025 = 0.24Total cost = 96 + 0.24 = Rs 96.24 Verification Brokerage added after discount reflects the actual purchase cost per Rs 100 face. Common pitfalls Applying brokerage to face value instead of market price. Interpreting 4 discount as 4 percent off an arbitrary base rather than Rs 4 below par for this context. Final Answer Rs 96.24

Question 8

A 12% stock yielding 10% is quoted at what price?

Accepted Answer

Concept / Approach Dividend is paid on face value; yield is income as a percentage of the market value. For one Rs. 100 stock paying 12% dividend, the annual income is Rs. 12. If the yield is 10%, then Rs. 12 must be 10% of the market price. Step-by-step calculationYield = (Dividend / Market value) × 10010 = (12 / P) × 100P = (12 × 100) / 10 = 120 VerificationAt price Rs. 120, income 12 gives yield 12/120 = 0.10 = 10%. Common pitfalls Using face value instead of market value in the yield formula. Final AnswerRs. 120

Question 9

A 10.5% stock gives an income of Rs. 756 from an outlay of Rs. 9000; brokerage is 1/4%. What is the market value per Rs. 100 stock?

Accepted Answer

Given data Dividend rate = 10.5% on face value Rs. 100 ⇒ income per Rs. 100 stock = Rs. 10.50. Total cash paid (including brokerage) = Rs. 9000. Brokerage = 0.25% on the purchase amount. Concept / Approach Let N be the number of Rs. 100 stocks; then income = 10.5 × N = 756 ⇒ find N. If x is the market price per Rs. 100 (before brokerage), total outlay = N × x × (1 + 0.0025). Step-by-step calculation10.5N = 756 ⇒ N = 756 / 10.5 = 72 (hundreds of stock)N × x × 1.0025 = 9000 ⇒ x = 9000 / (72 × 1.0025)x = 9000 / 72.18 ≈ 124.688… ⇒ 124.69 (to 2 decimals) VerificationCost before brokerage ≈ 72 × 124.688 = 8977.5; adding 0.25% ⇒ 8977.5 × 1.0025 ≈ 9000 (matches). Common pitfalls Ignoring brokerage or applying it to face value instead of the purchase amount. Final AnswerRs. 124.69

Question 10

To earn Rs. 650 from 10% stock quoted at Rs. 96 (no brokerage), how much must be invested?

Accepted Answer

Concept / Approach Dividend is on face value: 10% of Rs. 100 = Rs. 10 per Rs. 100 stock. Let N be the number of Rs. 100 stocks required; income = 10 × N = 650 ⇒ find N, then multiply by market price 96. Step-by-step calculation10N = 650 ⇒ N = 65Investment = 65 × 96 = 6240 VerificationIncome = 65 × 10 = Rs. 650 as needed. Final AnswerRs. 6,240

Question 11

A man bought 20 shares of Rs. 50 at Rs. 5 discount; the dividend rate is 13½%. What is the yield (rate of interest) on his investment?

Accepted Answer

Given data Face value per share = Rs. 50; purchase price = Rs. 45 (Rs. 5 discount). Dividend rate = 13.5% on face value ⇒ dividend per share = 0.135 × 50 = Rs. 6.75. Concept / Approach Yield (%) = (dividend per share / market price) × 100. Step-by-step calculationYield = (6.75 / 45) × 100 = 15% Notes The number of shares (20) cancels when computing percentage yield. Final Answer15%

Question 12

Rs. 20 shares pay 9% dividend. If an investor wants a 12% return, what should be the market value per share?

Accepted Answer

Concept / Approach Dividend per share = 9% of Rs. 20 = Rs. 1.80. Desired yield 12% ⇒ 1.80 should be 12% of the market price P. Step-by-step calculation1.80 / P × 100 = 12 ⇒ P = (1.80 × 100) / 12 = 15 Final AnswerRs. 15

Question 13

A man invests Rs. 1552 in a stock at 97 to obtain an income of Rs. 128. What is the dividend rate of the stock?

Accepted Answer

Given data Market price = Rs. 97 per Rs. 100 face value. Total outlay = Rs. 1552; income = Rs. 128. Concept / Approach First find the nominal (face) value purchased, then deduce the dividend rate from the income. Step-by-step calculationNominal purchased = (1552 / 97) × 100 = 1600 (since 97 × 16 = 1552)Let dividend rate be r%. Income = r% of 1600 = (r / 100) × 1600 = 16r16r = 128 ⇒ r = 8% VerificationAt 8% on Rs. 1600, income = 128 as given. Final Answer8%

Question 14

Rs. 9800 is invested partly in 9% stock at 75 and partly in 10% stock at 80 so that the incomes are equal. How much is invested in the 9% stock?

Accepted Answer

Let x = amount invested in 9% at 75; then (9800 − x) in 10% at 80. Income from each part Nominal bought from x: (x/75) × 100; annual income = 9% of this = 9x/75 = 3x/25. Nominal bought from (9800 − x): ((9800 − x)/80) × 100; income = 10% of this = (9800 − x)/8. Set incomes equal and solve3x/25 = (9800 − x)/824x = 25(9800 − x) ⇒ 24x = 245000 − 25x49x = 245000 ⇒ x = 5000 VerificationIncome from 9% part = 3×5000/25 = 600; from 10% part = (9800−5000)/8 = 4800/8 = 600 (equal). Final AnswerRs. 5,000

Question 15

A man invests Rs. 4455 in Rs. 10 shares quoted at Rs. 8.25. If the dividend rate is 12%, what is his annual income?

Accepted Answer

Step-by-step calculation Number of shares bought = 4455 / 8.25 = 540. Dividend per share = 12% of face value 10 = Rs. 1.20. Annual income = 540 × 1.20 = Rs. 648. Quick reasonableness check Yield = 648 / 4455 ≈ 14.55% (plausible since price is below face value and dividend is 12%). Final AnswerRs. 648

Question 16

Stocks & shares — compute yield (return on investment): A person buys a 4.5% stock at ₹96 (per ₹100 nominal). What percentage yield does the investor actually obtain on the investment?

Accepted Answer

Introduction / Context:In stock problems, the printed rate (e.g., 4.5%) is paid on the nominal value, typically ₹100. But investors pay the market price (here ₹96). The effective yield equals annual dividend divided by the investment, expressed as a percentage. Given Data / Assumptions: Nominal (face) value considered per unit = ₹100. Coupon rate = 4.5% ⇒ annual dividend per ₹100 nominal = ₹4.50. Market price paid = ₹96 per ₹100 nominal. Concept / Approach:Yield % = (Dividend received per unit / Price paid per unit) * 100. Step-by-Step Solution:Dividend per ₹100 nominal = ₹4.50.Price per ₹100 nominal = ₹96.Yield % = (4.50 / 96) * 100 = 4.6875% ≈ 4.69%. Verification / Alternative check:If you invest ₹96, you get ₹4.50 annually. Over ₹100 investment, that is 4.6875%. Rounding to two decimals yields 4.69%. Why Other Options Are Wrong: 4% and 4.5% ignore the price difference between nominal and market values. 1/2% is unrelated to the given coupon and price. Common Pitfalls: Using 4.5% directly as the yield instead of adjusting for the market price. Final Answer:4.69%

Question 17

Find the quoted price (market value): By investing ₹1100 in a 5.5% stock, an investor earns ₹77 per year. At what price (per ₹100 nominal) was the stock quoted?

Accepted Answer

Introduction / Context:Dividend is paid on nominal value, but you pay the quoted market price. Given actual income and total money invested, we can back-calculate the market price per ₹100 nominal. This is a classic inversion of the yield formula. Given Data / Assumptions: Total investment (cash outlay) = ₹1100. Coupon rate = 5.5% ⇒ dividend ₹5.50 per ₹100 nominal. Actual annual income = ₹77. Concept / Approach:If the market price is P per ₹100 nominal, then the number of ₹100-nominal units purchased is 1100 / P. Income = (1100 / P) * 5.5. Solve for P so that income equals ₹77. Step-by-Step Solution:Income equation: (1100 / P) * 5.5 = 77.Rearrange: 1100 * 5.5 = 77 * P.Compute 1100 * 5.5 = 6050.Thus P = 6050 / 77 = 78 + 44/77 = 78 4/7. Verification / Alternative check:At P = ₹78 4/7, number of shares = 1100 / (78 4/7) = 1100 / (550/7) = 14. Income = 14 * 5.5 = ₹77, confirming the result exactly. Why Other Options Are Wrong: Rs. 93 and Rs. 107 do not satisfy the income equation. Rs. 97 3/4 corresponds to a much lower yield than observed. Common Pitfalls: Treating ₹1100 as nominal instead of market investment, or mixing up yield with coupon rate. Final Answer:Rs. 78 4/7

Question 18

Required investment for target income: To produce an annual income of ₹500 from a 4% stock quoted at 90, how much money must be invested (market investment)?

Accepted Answer

Introduction / Context:You want a fixed income from a stock that pays a fixed percentage on nominal value but trades at a market price. The investment required depends on the relation between coupon rate and quoted price. Given Data / Assumptions: Target annual income = ₹500. Stock rate = 4% paid on nominal ₹100 ⇒ ₹4 dividend per ₹100 nominal. Market price = ₹90 per ₹100 nominal. Concept / Approach:Let I be the total investment. Then the number of ₹100-nominal units purchased is I / 90. Annual income = (I / 90) * 4. Set equal to ₹500 and solve for I. Step-by-Step Solution:(I / 90) * 4 = 500.I = 500 * 90 / 4 = 500 * 22.5 = ₹11250. Verification / Alternative check:At I = ₹11250, number of units = 11250 / 90 = 125. Income = 125 * 4 = ₹500, confirming the requirement. Why Other Options Are Wrong: ₹12500, ₹18000, ₹20000 yield incomes different from ₹500 at 4% with price 90. Common Pitfalls: Using 4% on the investment directly (which would be wrong since 4% applies to nominal, not market price). Final Answer:Rs. 11250

Question 19

Market value from yield relation: A 4% stock is providing a 5% yield to an investor. What is the market value (price per ₹100 nominal)?

Accepted Answer

Introduction / Context:The stock's coupon rate is paid on nominal value, but yield compares that dividend to the price paid. If a 4% stock yields 5%, the investor must be buying below par. The price can be computed directly by proportion. Given Data / Assumptions: Coupon rate = 4% ⇒ ₹4 dividend per ₹100 nominal. Observed yield = 5% on the actual price. Concept / Approach:Yield % = (Dividend / Price) * 100. Rearranged: Price = (Dividend * 100) / Yield% = (4 * 100) / 5 = ₹80. Step-by-Step Solution:Dividend per ₹100 = ₹4.Yield% = 5 ⇒ Price = 4 * 100 / 5 = ₹80. Verification / Alternative check:At ₹80 price, income ₹4 gives 4/80 * 100 = 5% yield, which matches the given yield. Why Other Options Are Wrong: ₹125 implies a yield below 4% for a 4% coupon, which contradicts 5% yield. ₹99 and ₹109 do not give the exact 5% yield. Common Pitfalls: Mistaking coupon for yield; yield depends on market price, not just coupon. Final Answer:Rs. 80

Question 20

Required investment for target income — 6% stock at 96: What investment (in ₹) is needed to secure an annual income of ₹100?

Accepted Answer

Introduction / Context:Given a coupon rate and a quoted price, compute how much cash must be invested to produce a specific income. This reverses the usual yield calculation. Given Data / Assumptions: Coupon rate = 6% ⇒ ₹6 per ₹100 nominal per year. Market price = ₹96 per ₹100 nominal. Target income = ₹100 per year. Concept / Approach:If I is the investment, the number of ₹100-nominal units = I / 96. Income = (I / 96) * 6. Set equal to 100 and solve I = 100 * 96 / 6. Step-by-Step Solution:(I / 96) * 6 = 100.I = 100 * 96 / 6 = 1600. Verification / Alternative check:At investment ₹1600, units = 1600/96 = 16.666… of ₹100 nominal; income = 16.666… * 6 = ₹100, confirming the target. Why Other Options Are Wrong: ₹1504 and ₹1666.66 produce different incomes than ₹100 for a 6% coupon at ₹96 price. ₹5760 is not related to the small income target given the high coupon. Common Pitfalls: Treating 6% as applied to the investment instead of nominal value. Final Answer:Rs. 1600

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