Question 1

Investment required for a bond/stock purchase: How much cash is required to purchase $125,000 nominal of 8% stock at a market price of 92 (i.e., $92 per $100 nominal)?

Accepted Answer

Introduction / Context: Quoted prices for fixed-interest stock are typically per $100 nominal. To find the cash outlay for a desired nominal amount, scale the quoted price accordingly. The coupon rate is irrelevant to the cash needed for the purchase. Given Data / Assumptions: Nominal (par) to be purchased = $125,000. Quoted price = 92 per $100 nominal. Concept / Approach: Investment = Nominal * (Quoted price / 100). Multiply the nominal target by 0.92 to get the total cash outlay, ignoring brokerage and taxes (not mentioned). Step-by-Step Solution: Investment = 125,000 * 92 / 100 = 125,000 * 0.92 = $115,000. Verification / Alternative check: Each $100 nominal costs $92; for 1,250 hundreds, pay 1,250 * $92 = $115,000. Why Other Options Are Wrong: $120,000, $105,000, and $118,000 do not match 92% of $125,000; $125,000 is the cost at par, not at 92. Common Pitfalls: Treating 92 as 0.92 dollars instead of 92 per hundred, or mixing nominal and cash amounts. Final Answer: $ 115000

Question 2

A man buys Rs 20 shares that pay a 9% annual dividend. He wants to earn 12% interest on his investment. What should be the market value of each share?

Accepted Answer

Introduction / Context: This problem belongs to the topic of stocks and shares. It tests understanding of how dividend, face value, market value, and required rate of return are related. Such questions are very common in banking and finance related aptitude tests. Given Data / Assumptions: Face value of each share = Rs 20. Dividend rate = 9 percent per annum on face value. The investor wants a 12 percent return on the money he actually invests, that is, on the market value. We assume dividends are paid once a year and there are no additional taxes or charges. Concept / Approach: Dividend is calculated on the face value, but the investor pays the market value. The effective yield or return is (annual dividend / market value) * 100 percent. To achieve a desired yield, we equate this expression to the required percentage and solve for the market value. Step-by-Step Solution: Step 1: Compute the annual dividend per share.Step 2: Dividend = 9 percent of Rs 20 = (9/100) * 20 = Rs 1.80 per share.Step 3: Let the market value of each share be Rs P.Step 4: The investor wants a 12 percent return, so yield = (dividend / P) * 100 = 12.Step 5: Substitute dividend = 1.80: (1.80 / P) * 100 = 12.Step 6: Simplify: 180 / P = 12.Step 7: Solve for P: P = 180 / 12 = 15.Step 8: Therefore, the market value of each share should be Rs 15. Verification / Alternative check: Check the yield if the market price is Rs 15: yield = (1.80 / 15) * 100 percent. Compute 1.80 / 15 = 0.12, then 0.12 * 100 percent = 12 percent. This matches the investor requirement, confirming the correctness of the result. Why Other Options Are Wrong: Rs 12: If P = 12, yield would be (1.80 / 12) * 100 = 15 percent, which is higher than required. Rs 18: If P = 18, yield would be (1.80 / 18) * 100 = 10 percent, lower than required. Rs 20: If P = 20, yield would be (1.80 / 20) * 100 = 9 percent, which is just the dividend rate, not the desired 12 percent on investment. Common Pitfalls: Students sometimes mistakenly compute dividend on the market value instead of face value, or they confuse dividend rate with required yield. It is crucial to remember that dividend is always declared on face value, while the investor cares about return on the actual price paid in the market. Final Answer: The market value of each share should be Rs 15.

Question 3

A 6% stock yields an 8% return on the investor's money. What is the market value (price per Rs. 100 nominal) of this stock?

Accepted Answer

Introduction / Context: Questions on stocks and shares often test the relationship between the nominal (face) value of a share, its dividend rate, the market value, and the effective yield on an investor's money. Here, we are given the dividend rate of the stock and the yield actually obtained by the investor, and we are asked to find the market value of the stock that produces such a yield. Given Data / Assumptions: The nominal (face) value of the stock is taken as Rs. 100. The dividend rate on the stock is 6% per year. The investor's yield on investment is 8% per year. We assume standard convention that a 6% stock means Rs. 6 dividend per year on Rs. 100 nominal value. Concept / Approach: For a stock, dividend is always calculated on the nominal value, while yield is calculated on the actual money invested (market value). If the annual dividend on Rs. 100 nominal is D and the market price is P, then the yield on investment is given by: yield % = (D / P) * 100 In this problem we know the dividend rate (6%) and the yield (8%). We use the above formula to solve for the unknown market value P. Step-by-Step Solution: Step 1: Take the nominal value of the stock as Rs. 100. Step 2: Since it is a 6% stock, annual dividend on Rs. 100 nominal is D = 6% of 100 = Rs. 6. Step 3: Let P be the market value (price) of this Rs. 100 stock. Step 4: Given that the yield on investment is 8%, we write: (6 / P) * 100 = 8. Step 5: Simplify: 6 / P = 8 / 100 = 0.08. Step 6: Therefore, P = 6 / 0.08 = 75. Step 7: Thus the market value of the Rs. 100 stock must be Rs. 75. Verification / Alternative check: If the stock is bought at Rs. 75 and pays Rs. 6 as annual dividend, then the actual yield is: yield % = (6 / 75) * 100 = 8% This agrees exactly with the given yield in the problem, so our answer is consistent. Why Other Options Are Wrong: Rs. 48 would give a yield of (6 / 48) * 100 = 12.5%, which is greater than 8%, so it is not correct. Rs. 96 would give a yield of (6 / 96) * 100 = 6.25%, which is less than 8%. Rs. 133.33 would produce an even smaller yield of about 4.5%. Rs. 50 would give a yield of 12%, also inconsistent. Only Rs. 75 satisfies the required 8% yield. Common Pitfalls: Students sometimes confuse the dividend rate with the yield on investment and try to apply 8% on Rs. 100 directly. Another frequent mistake is to assume that the market value must exceed the nominal value, which is not always true. It is important to remember that dividend is calculated on nominal value, while yield is calculated based on the current market price actually paid by the investor. Final Answer: The market value of the stock is Rs. 75 per Rs. 100 nominal value.

Question 4

In order to obtain an annual income of Rs. 650 from a 10% stock quoted at Rs. 96, how much money must an investor invest in the stock?

Accepted Answer

Introduction / Context: This question checks understanding of how to compute the amount of money that must be invested in a stock in order to obtain a desired annual income. The key idea is that dividend is based on nominal value while the money actually invested depends on the quoted market price of the stock. We combine both ideas to back-calculate the required investment for a target income. Given Data / Assumptions: Dividend rate = 10% stock, meaning Rs. 10 dividend per Rs. 100 nominal value. Market price (quoted value) of the stock = Rs. 96 per Rs. 100 nominal. Required annual income from dividends = Rs. 650. No brokerage or additional charges are mentioned, so we ignore them. Concept / Approach: The annual dividend for Rs. 100 nominal is given directly by the dividend rate. To earn a target dividend, we first find the total nominal value of stock required. Once we know the total nominal value, we multiply by the market price per Rs. 100 nominal to obtain the actual cash investment. The steps are: 1. Use dividend rate to find nominal value required. 2. Use quoted price to convert nominal value into actual investment. Step-by-Step Solution: Step 1: Dividend on Rs. 100 nominal at 10% stock = Rs. 10 per year. Step 2: Let the total nominal value of stock purchased be N rupees. Step 3: Then annual dividend = 10% of N = (10 / 100) * N = N / 10. Step 4: We want this dividend to equal the required income of Rs. 650, so N / 10 = 650. Step 5: Therefore N = 650 * 10 = Rs. 6,500 nominal. Step 6: Market price is Rs. 96 per Rs. 100 nominal. So investment per Rs. 100 nominal = Rs. 96. Step 7: For Rs. 6,500 nominal, the actual investment = (6500 / 100) * 96 = 65 * 96 = Rs. 6,240. Verification / Alternative check: If the investor puts Rs. 6,240 into the 10% stock at Rs. 96, nominal value purchased is (6240 / 96) * 100 = Rs. 6,500 nominal. The annual dividend on Rs. 6,500 nominal at 10% is 0.10 * 6500 = Rs. 650, which matches the required income. So the calculation is consistent. Why Other Options Are Wrong: Rs. 3,100 corresponds to only half the required nominal value and would yield Rs. 325. Rs. 6,500 is the nominal value, not the cash invested. Rs. 9,600 corresponds to buying Rs. 10,000 nominal, giving Rs. 1,000 dividend. Rs. 5,200 represents an incorrect combination of nominal and market price. Only Rs. 6,240 correctly matches the target income of Rs. 650 at the given price and dividend rate. Common Pitfalls: Common errors include applying 10% directly on the invested amount (ignoring that dividend is on nominal value) or assuming that Rs. 6,500 must be the investment instead of the nominal value. Another mistake is forgetting to scale nominal value by the quoted price per Rs. 100 when computing the actual cash investment. Final Answer: The investor must invest Rs. 6,240 in the 10% stock quoted at Rs. 96 to obtain an income of Rs. 650 per year.

Question 5

The cost price of a Rs. 100 face value stock quoted at a discount of Rs. 4, when brokerage is 1/4%, is equal to how many rupees per Rs. 100 nominal?

Accepted Answer

Introduction / Context: This problem tests understanding of how to calculate the effective cost price of a stock when both a discount and brokerage are involved. Discount affects the quoted market price, while brokerage is an additional charge paid to the broker, usually calculated as a percentage of the nominal value or the market value depending on convention. Given Data / Assumptions: Face (nominal) value of the stock = Rs. 100. The stock is quoted at a discount of Rs. 4, so quoted price = Rs. 96. Brokerage rate = 1/4% (that is, 0.25%). We assume brokerage is charged on the nominal value of Rs. 100, as is common in many exam problems. Concept / Approach: The total cost price for an investor buying Rs. 100 nominal of stock is the sum of the market price and brokerage. If P is the quoted market value and B is the brokerage per Rs. 100 nominal, then: effective cost price = P + B We first find the quoted price after discount, then compute brokerage, and finally add the two to obtain the cost price per Rs. 100 nominal. Step-by-Step Solution: Step 1: Since the stock is at a discount of Rs. 4 on Rs. 100 nominal, quoted price P = 100 - 4 = Rs. 96. Step 2: Brokerage rate = 1/4% = 0.25% on Rs. 100 nominal. Step 3: Brokerage per Rs. 100 nominal B = (0.25 / 100) * 100 = Rs. 0.25. Step 4: Effective cost price per Rs. 100 nominal = P + B = 96 + 0.25 = Rs. 96.25. Step 5: Therefore, the investor effectively pays Rs. 96.25 for each Rs. 100 nominal of stock purchased. Verification / Alternative check: One can check by imagining purchase of several shares. For one Rs. 100 share, the investor pays Rs. 96 as price and Rs. 0.25 as brokerage, totalling Rs. 96.25. For any number of shares, the effective cost per Rs. 100 nominal remains Rs. 96.25, confirming the calculation. Why Other Options Are Wrong: Rs. 95.75 would imply subtracting brokerage instead of adding it, which is incorrect. Rs. 96 ignores brokerage entirely. Rs. 104.25 is higher than the nominal value and does not match any reasonable combination of discount and brokerage here. Rs. 100 corresponds to purchasing at par without discount or brokerage. Only Rs. 96.25 correctly incorporates both the Rs. 4 discount and the 1/4% brokerage on Rs. 100 nominal. Common Pitfalls: Students often calculate brokerage on the market price instead of the nominal value when the question implies otherwise, or they mistakenly subtract brokerage in a purchase scenario. It is important to read carefully whether brokerage is added to or subtracted from the price and whether it is calculated on face value or on market value. Final Answer: The correct cost price is Rs. 96.25 per Rs. 100 nominal of stock.

Question 6

By investing Rs. 1,620 in an 8% stock, Michael earns Rs. 135 as annual dividend. At what market price per Rs. 100 nominal is the stock quoted?

Accepted Answer

Introduction / Context: This question examines how to connect the amount of money invested in a stock, the annual dividend received, and the market price of the stock. The stock pays a stated percentage dividend on its nominal value, and the investor's income and investment together allow us to work backward to the quoted market value per Rs. 100 nominal. Given Data / Assumptions: Dividend rate = 8% stock, meaning Rs. 8 dividend per Rs. 100 nominal. Total money invested by Michael = Rs. 1,620. Annual dividend income = Rs. 135. We assume there is no brokerage or other cost. Concept / Approach: If the market price per Rs. 100 nominal is P rupees, then investing P rupees buys Rs. 100 nominal of stock and yields dividend of Rs. 8. If the investor puts in K rupees, the total nominal value purchased is (K / P) * 100 and the dividend earned is (K / P) * 8. Setting this equal to the given income allows us to solve for P. The relationship can be written as: (K / P) * 8 = given income Step-by-Step Solution: Step 1: Let P be the market price per Rs. 100 nominal. Step 2: For each P rupees invested, the investor gets Rs. 8 dividend (because the stock is 8% on Rs. 100 nominal). Step 3: Michael invests K = Rs. 1,620. Then his annual dividend income is (1620 / P) * 8. Step 4: Set this equal to the given income: (1620 / P) * 8 = 135. Step 5: Simplify: 1620 * 8 = 135 * P. Step 6: Compute the product: 1620 * 8 = 12,960. Step 7: So 12,960 = 135 * P, hence P = 12,960 / 135 = Rs. 96. Verification / Alternative check: If P = Rs. 96, then with Rs. 1,620 Michael buys (1620 / 96) * 100 = Rs. 1,687.50 nominal of stock. The dividend on this nominal value at 8% is 0.08 * 1687.5 = Rs. 135, which matches the given income. Therefore the quoted price of Rs. 96 is correct. Why Other Options Are Wrong: At Rs. 80, the dividend would be higher than Rs. 135 because more nominal value could be bought. At Rs. 106 or Rs. 108, the amount of nominal stock purchased would be lower and the dividend would be less than Rs. 135. A price of Rs. 120 would reduce the nominal even further and give still lower income. Only Rs. 96 satisfies the income condition exactly. Common Pitfalls: A frequent mistake is to treat 8% as the yield on investment instead of the dividend on nominal value. Another error is attempting to divide income by the dividend rate directly without considering the market price factor. Always form an equation based on income = (investment / market price) * dividend per Rs. 100 nominal. Final Answer: The stock is quoted at a market value of Rs. 96 per Rs. 100 nominal.

Question 7

A man invests Rs. 14,400 in Rs. 100 shares of a company that are selling at a 20% premium. If the company declares a 5% dividend on the face value at year end, what total dividend does he receive?

Accepted Answer

Introduction / Context: This problem combines the ideas of premium on shares and dividend on nominal value. The investor buys shares that are quoted above their face value, but the dividend is still calculated on the face value. We must determine the number of shares purchased and then compute the dividend from the declared percentage rate. Given Data / Assumptions: Investment amount = Rs. 14,400. Face value of each share = Rs. 100. Shares are at 20% premium, so market price per share = Rs. 120. Dividend declared = 5% on face value. No brokerage or taxes are mentioned, so they are ignored. Concept / Approach: First, we find how many shares the man can buy at the given premium price. Since dividend is calculated on face value, we then multiply the total nominal value of all shares by the dividend rate. Key formulas are: number of shares = total investment / market price per share dividend per share = (dividend rate % of face value) Step-by-Step Solution: Step 1: Market price per share = face value + 20% of face value = 100 + 0.20 * 100 = Rs. 120. Step 2: Number of shares purchased = 14,400 / 120 = 120 shares. Step 3: Dividend per share at 5% on Rs. 100 face value = 0.05 * 100 = Rs. 5. Step 4: Total dividend received = number of shares * dividend per share = 120 * 5. Step 5: Compute 120 * 5 = Rs. 600. Step 6: Therefore, the investor receives Rs. 600 as total annual dividend. Verification / Alternative check: Total nominal value of the shares is 120 * 100 = Rs. 12,000. A 5% dividend on Rs. 12,000 is 0.05 * 12000 = Rs. 600, confirming our computation. The fact that he invested Rs. 14,400 simply reflects the 20% premium he paid above face value. Why Other Options Are Wrong: Rs. 500 and Rs. 560 do not correspond to 5% of any reasonable total nominal value based on the given numbers. Rs. 650 and Rs. 720 would require either a higher dividend percentage or a different number of shares than is possible with the given investment and premium. Only Rs. 600 matches 5% of the correct total nominal value Rs. 12,000. Common Pitfalls: Many learners mistakenly calculate the dividend on the market price (Rs. 120) instead of the face value (Rs. 100). Others try to take 5% of the total investment of Rs. 14,400, which is incorrect. Always remember that when a company declares a dividend of a certain percent, it is almost always on the face (nominal) value of the shares, not on the market value. Final Answer: The man receives a total dividend of Rs. 600 at the end of the year.

Question 8

Find the cash realised by selling Rs. 2,440 nominal of 9.5% stock at a 4% discount, if brokerage is 1/4% on the market value.

Accepted Answer

Introduction / Context: This question focuses on finding the net cash realised when selling a block of stock at a discount, after deducting brokerage. The holder has a certain nominal amount of 9.5% stock, but the dividend rate is not needed here because we are only concerned with sale proceeds, market value, and brokerage. Given Data / Assumptions: Nominal (face) value of stock sold = Rs. 2,440. The stock is sold at a 4% discount, so market price per Rs. 100 nominal is Rs. 96. Brokerage rate on sale = 1/4% = 0.25% of the market value. We assume brokerage is deducted from the gross sale proceeds to find net cash realised. Concept / Approach: First find the gross sale value using the discounted market price. Then compute brokerage as a percentage of this gross value and subtract it to get net cash realised. The main formulas are: gross sale value = nominal value * (market price per 100 / 100) brokerage = brokerage rate * gross sale value net cash realised = gross sale value - brokerage Step-by-Step Solution: Step 1: Market price per Rs. 100 nominal at 4% discount = 100 - 4 = Rs. 96. Step 2: Gross sale value for Rs. 2,440 nominal = 2440 * (96 / 100) = 2440 * 0.96 = Rs. 2,342.40. Step 3: Brokerage rate = 0.25% of gross sale value. Step 4: Brokerage amount = 0.25 / 100 * 2342.40 = 2342.40 * 0.0025 = Rs. 5.856. Step 5: Net cash realised = gross sale value - brokerage = 2342.40 - 5.856 = Rs. 2,336.544. Step 6: Rounding to two decimal places, net cash realised ≈ Rs. 2,336.54. Verification / Alternative check: We can check orders of magnitude: selling at Rs. 96 per Rs. 100 nominal means roughly 96% of Rs. 2,440, which is around Rs. 2,342. Deducting a very small brokerage of 0.25% of this amount must reduce the proceeds by less than Rs. 10. Subtracting a little under Rs. 6 gives about Rs. 2,336, so Rs. 2,336.54 is consistent with this approximation. Why Other Options Are Wrong: Values like Rs. 2,289.00 and Rs. 2,290.00 are too low and would correspond to a much larger effective discount or brokerage. Rs. 2,305.75 also implies higher charges than those given. Rs. 2,400.00 would be greater than the gross sale value at a discount, which is impossible. Only Rs. 2,336.54 is consistent with 4% discount and 0.25% brokerage. Common Pitfalls: Students may mistakenly compute brokerage on the face value instead of the market value, or they may add brokerage instead of subtracting it when dealing with a sale. It is crucial to distinguish purchase problems, where brokerage is added to cost, from sale problems, where brokerage reduces the cash received. Final Answer: The cash realised by selling the stock is approximately Rs. 2,336.54.

Question 9

A man invests in a 16% stock quoted at Rs. 128 per Rs. 100 nominal. What percentage return (yield) does he obtain on his investment?

Accepted Answer

Introduction / Context: This problem asks for the effective yield on an investment in shares when the dividend rate and the market price are known. The investor buys a 16% stock at a market price above its face value. Because yield is calculated on the money actually invested (market price), investing at a premium generally reduces the effective return compared to the nominal dividend rate. Given Data / Assumptions: Dividend rate = 16% stock, so dividend on Rs. 100 nominal is Rs. 16 per year. Market price = Rs. 128 per Rs. 100 nominal. No brokerage or additional expenses are mentioned. We must find the percentage yield on the investor's money. Concept / Approach: Yield on investment is defined as: yield % = (annual income from investment / amount invested) * 100 For one Rs. 100 share, annual income is Rs. 16 and the amount invested is the market price Rs. 128. We substitute these numbers into the yield formula to find the effective percentage return. Step-by-Step Solution: Step 1: For a Rs. 100 nominal share, annual dividend at 16% = 16% of 100 = Rs. 16. Step 2: Market price per share = Rs. 128. Step 3: Yield on investment for one share = (annual income / amount invested) * 100. Step 4: Substitute values: yield % = (16 / 128) * 100. Step 5: Simplify 16 / 128 = 1 / 8. Step 6: Therefore, yield % = (1 / 8) * 100 = 12.5%. Verification / Alternative check: If the investor bought any number of shares, the ratio of total dividend to total investment would be the same because both scale proportionally. For example, buying 10 such shares costs 10 * 128 = Rs. 1,280 and yields 10 * 16 = Rs. 160. Then yield % = (160 / 1280) * 100 = 12.5%, confirming our result. Why Other Options Are Wrong: 8% and 10% are lower than the true yield and do not match the ratio 16 / 128. A yield of 16% would only occur if the stock were bought at par (Rs. 100), not at a premium. 12% is close but still incorrect because 16 / 128 simplifies exactly to 1 / 8, giving 12.5%. Only 12.5% fits the numerical relationship. Common Pitfalls: Learners sometimes confuse the dividend rate with yield and answer 16% directly. Another error is to divide the market price by the dividend, reversing the correct ratio. Always remember that yield is income divided by amount invested, multiplied by 100 to express it as a percentage. Final Answer: The investor obtains a yield of 12.5% on his investment.

Question 10

A man sells Rs. 5,000 nominal of 12% stock at Rs. 156 and receives Rs. 7,800. He reinvests the proceeds partly in 8% stock at Rs. 90 and partly in 9% stock at Rs. 108, thereby increasing his annual income by Rs. 70. How much of the proceeds are inve…

Accepted Answer

Introduction / Context: This is a classic stocks and shares word problem involving sale of an existing investment and reinvestment of the proceeds into two different stocks. The key challenge is to relate the original dividend income and the new dividend income so that we can determine how the proceeds were split between the two new stocks. The question combines concepts of nominal value, market value, and dividend yield. Given Data / Assumptions: Original holding: Rs. 5,000 nominal of 12% stock. Selling price of original stock = Rs. 156 per Rs. 100 nominal. Proceeds from sale = 5000 * 156 / 100 = Rs. 7,800. New stocks: 8% stock at Rs. 90 and 9% stock at Rs. 108. Increase in annual income after reinvestment = Rs. 70. No brokerage is mentioned, so it is ignored. Concept / Approach: First find the original annual income from the 12% stock. Then express the new income from the two investments in terms of the unknown amounts invested in the 8% and 9% stocks. Setting new income equal to old income plus Rs. 70 gives a linear equation that can be solved for one of the investment amounts. The remainder of the proceeds is invested in the other stock. Step-by-Step Solution: Step 1: Original income from 12% stock = 12% of Rs. 5,000 nominal = (12 / 100) * 5000 = Rs. 600. Step 2: Total sale proceeds = 5000 * 156 / 100 = Rs. 7,800. Step 3: Let x rupees be invested in 8% stock at Rs. 90. Then income from this part = (x / 90) * 8. Step 4: Remaining amount invested in 9% stock = 7800 - x. Income from this part = ((7800 - x) / 108) * 9. Step 5: Total new income = (x / 90) * 8 + ((7800 - x) / 108) * 9. Step 6: New income is greater than old income by Rs. 70, so: (x / 90) * 8 + ((7800 - x) / 108) * 9 = 600 + 70 = 670. Step 7: Simplify each term: (8x / 90) = (4x / 45) and (9(7800 - x) / 108) = (7800 - x) / 12. Step 8: So the equation becomes 4x / 45 + (7800 - x) / 12 = 670. Step 9: Solve this equation to get x = Rs. 3,600. Step 10: Therefore, investment in 8% stock = Rs. 3,600 and investment in 9% stock = 7,800 - 3,600 = Rs. 4,200. Verification / Alternative check: Income from Rs. 3,600 in 8% stock at Rs. 90: nominal value = (3600 / 90) * 100 = Rs. 4,000, income = 8% of 4,000 = Rs. 320. Income from Rs. 4,200 in 9% stock at Rs. 108: nominal value = (4200 / 108) * 100 = Rs. 3,888.89 approximately, income ≈ 9% of 3,888.89 ≈ Rs. 350. New total income ≈ 320 + 350 = Rs. 670, which is Rs. 70 more than the original Rs. 600. Why Other Options Are Wrong: Exchanging the two amounts (as in option B) changes the nominal values and gives a different income. The other splits such as (4,000, 3,800) or (5,000, 2,800) do not satisfy the required increase of Rs. 70 in total income when proper yield calculations are performed. Only Rs. 3,600 in 8% stock and Rs. 4,200 in 9% stock produce the correct increment. Common Pitfalls: Students may incorrectly assume that income is directly proportional to money invested without adjusting for different market prices. Another mistake is to use the percentage on the invested amount instead of on the nominal value. Careful formulation of income expressions for each stock is critical to solving such problems correctly. Final Answer: The man invests Rs. 3,600 in 8% stock and Rs. 4,200 in 9% stock.

Question 11

A 12% stock is providing an investor a 10% yield on his money. At what market price per Rs. 100 nominal is this stock quoted?

Accepted Answer

Introduction / Context: This question is a straightforward application of the relationship between dividend rate, market price, and yield. A 12% stock paying dividend on its nominal value produces a 10% return on the investor's money when bought at a certain market price. We must find that quoted price per Rs. 100 nominal. Given Data / Assumptions: Dividend rate = 12% stock, so dividend on Rs. 100 nominal = Rs. 12 per year. Yield on investment (actual return) = 10% per year. No brokerage is mentioned, so we ignore any additional charges. Nominal value for comparison is taken as Rs. 100. Concept / Approach: The yield on investment is given by: yield % = (dividend per share / market price per share) * 100 Here, dividend per share (on Rs. 100 nominal) is Rs. 12, and the desired yield is 10%. We substitute into the formula and solve for the market price P. Rearranging gives: P = (dividend per share * 100) / yield % Step-by-Step Solution: Step 1: Dividend per Rs. 100 nominal = 12% of 100 = Rs. 12. Step 2: Desired yield on investment = 10%. Step 3: Let P be the market price per Rs. 100 nominal. Step 4: Use formula: 10 = (12 / P) * 100. Step 5: Rearrange: 12 / P = 10 / 100 = 0.10. Step 6: Therefore, P = 12 / 0.10 = Rs. 120. Verification / Alternative check: If an investor buys the stock at Rs. 120 and receives a dividend of Rs. 12 per Rs. 100 nominal, then yield on investment = (12 / 120) * 100 = 10%, exactly as required in the problem statement. This confirms that the quoted price must be Rs. 120. Why Other Options Are Wrong: At Rs. 67 or Rs. 100, the yield would be higher than 10% since the same dividend would be obtained for less investment. At Rs. 110 or Rs. 112, the yield would be slightly more than or less than 10%, but not exactly 10%. Only at Rs. 120 does the yield match the given 10% return on investment. Common Pitfalls: A common error is to assume that the percentage printed on the stock certificate (12%) is automatically the yield, ignoring the effect of buying at a premium or discount. Another mistake is reversing the ratio and computing 120 / 10 instead of using the correct formula. Always remember that yield is dividend divided by market price multiplied by 100. Final Answer: The stock is quoted at a market price of Rs. 120 per Rs. 100 nominal value.

Question 12

By investing Rs. 1,620 in an 8% stock, Michael earns Rs. 135 as annual dividend. At what market value per Rs. 100 nominal is the stock quoted?

Accepted Answer

Introduction / Context: This is another yield and market price question based on the same data as a previous example, but with different distractor options. The investor's total dividend and total investment are known, and we must determine the market value of an 8% stock that results in the observed income. Given Data / Assumptions: Michael invests Rs. 1,620 in an 8% stock. Annual dividend income = Rs. 135. Dividend rate = 8% on nominal value, so Rs. 8 per Rs. 100 nominal. No brokerage is mentioned. Concept / Approach: If P is the market price per Rs. 100 nominal, then investing P rupees buys Rs. 100 nominal and yields Rs. 8 in dividend. For an investment of 1,620 rupees, the number of hundreds of nominal value purchased is 1620 / P, and the total dividend is (1620 / P) * 8. We equate this to the known income of Rs. 135 and solve for P. Step-by-Step Solution: Step 1: Let P be the market price per Rs. 100 nominal. Step 2: Dividend from Rs. 1,620 investment = (1620 / P) * 8. Step 3: Given this dividend equals Rs. 135, so (1620 / P) * 8 = 135. Step 4: Multiply both sides by P: 1620 * 8 = 135 * P. Step 5: Compute the left side: 1620 * 8 = 12,960. Step 6: Therefore P = 12,960 / 135 = Rs. 96. Step 7: Hence the stock is quoted at Rs. 96 per Rs. 100 nominal. Verification / Alternative check: At P = 96, nominal value purchased = (1620 / 96) * 100 = Rs. 1,687.50. Dividend at 8% = 0.08 * 1687.5 = Rs. 135, which matches the given income. This confirms that Rs. 96 is the correct market value. Why Other Options Are Wrong: Rs. 75 or Rs. 80 would lead to a higher nominal value and hence a higher dividend than Rs. 135. Rs. 145 and Rs. 245.10 are too high; buying at those prices would reduce nominal holdings far below the level needed to generate Rs. 135 at 8%. Only Rs. 96 matches exactly with the stated investment and income. Common Pitfalls: Students may misinterpret 8% as yield on investment rather than on nominal value or attempt to divide 135 directly by 0.08 ignoring the market price relationship. Always use the proper formula linking investment, market price, nominal value, and dividend rate to avoid such errors. Final Answer: The stock is quoted at a market value of Rs. 96 per Rs. 100 nominal.

Question 13

Which is the better investment: an 11% stock quoted at Rs. 143 or a 9.75% stock quoted at Rs. 117, if you compare the effective yield on investment?

Accepted Answer

Introduction / Context: Many stock and shares questions ask you to compare two different investments and decide which is better. "Better" usually means that the investment gives a higher percentage return (yield) on the money invested, assuming risk and other factors are similar. Here we compare an 11% stock and a 9.75% stock, each quoted at a different market price. Given Data / Assumptions: First stock: 11% stock at a market price of Rs. 143 per Rs. 100 nominal. Second stock: 9.75% stock at a market price of Rs. 117 per Rs. 100 nominal. Dividend is calculated on nominal value; yield is calculated on market value. No brokerage is mentioned. Concept / Approach: We compute the yield for each stock individually using: yield % = (dividend per Rs. 100 nominal / market price) * 100 Then we compare the two yield percentages. The investment with the higher yield is the better one from a purely return-based perspective. Step-by-Step Solution: Step 1: For the 11% stock, dividend per Rs. 100 nominal = Rs. 11. Step 2: Market price = Rs. 143. Yield % for this stock = (11 / 143) * 100. Step 3: Compute 11 / 143 ≈ 0.07692, so yield ≈ 7.692%. Step 4: For the 9.75% stock, dividend per Rs. 100 nominal = Rs. 9.75. Step 5: Market price = Rs. 117. Yield % for this stock = (9.75 / 117) * 100. Step 6: Compute 9.75 / 117 ≈ 0.08333, so yield ≈ 8.333%. Step 7: Compare the yields: about 7.692% versus 8.333%. The second stock has the higher yield. Verification / Alternative check: If you imagine investing Rs. 1,430 in the first stock, you would buy 10 nominal lots of Rs. 100 and receive dividend 10 * 11 = Rs. 110. Yield ≈ 110 / 1430 * 100 ≈ 7.692%. Similarly, investing Rs. 1,170 in the second stock buys 10 nominal lots and yields 10 * 9.75 = Rs. 97.50, giving 97.5 / 1170 * 100 ≈ 8.333%. This again confirms that the second stock offers the better return. Why Other Options Are Wrong: They are not equally good because the yields differ. It is not true that they cannot be compared; yield calculation does not require a specific investment amount. Saying both give yield less than 5% is numerically false. The 11% stock at 143 is decent but still inferior to the 9.75% stock at 117 in terms of yield. Common Pitfalls: Students sometimes compare the nominal percentages only and conclude that 11% must be better, ignoring the effect of market price. Another mistake is to think that the total investment amount is needed; but yield is independent of scale. Always compute yield as dividend divided by market price to compare investments accurately. Final Answer: The better investment is the 9.75% stock quoted at Rs. 117.

Question 14

A man invests Rs. 4,455 in Rs. 10 shares that are quoted at Rs. 8.25. If the company declares a 12% dividend on face value, what is his annual dividend income?

Accepted Answer

Introduction / Context: This problem involves computing the number of shares bought at a quoted market price and then finding the annual dividend using a percentage rate on the face value. It reinforces two important ideas in stock calculations: market price determines how many shares can be purchased, while dividend is calculated on the nominal (face) value of the shares held. Given Data / Assumptions: Total investment = Rs. 4,455. Face value of each share = Rs. 10. Market price (quoted value) per share = Rs. 8.25. Dividend rate = 12% on face value. No brokerage is mentioned. Concept / Approach: First we find the number of shares purchased by dividing the total amount invested by the market price per share. Then we compute the total nominal value of those shares and apply the 12% dividend rate on this nominal value to obtain the annual dividend income. The main formulas are: number of shares = total investment / market price per share dividend per share = 12% of face value total dividend = number of shares * dividend per share Step-by-Step Solution: Step 1: Number of shares bought = 4455 / 8.25. Step 2: Compute 4455 / 8.25 = 540 shares. Step 3: Face value of each share = Rs. 10, so total nominal value = 540 * 10 = Rs. 5,400. Step 4: Dividend rate = 12% on face value. Step 5: Annual dividend per share = 12% of Rs. 10 = 0.12 * 10 = Rs. 1.20. Step 6: Total annual dividend = 540 * 1.20 = Rs. 648. Step 7: Therefore, the investor receives Rs. 648 per year as dividend. Verification / Alternative check: Instead of working per share, we could take 12% of the total nominal value. Nominal value is Rs. 5,400, and 12% of 5,400 is 0.12 * 5400 = Rs. 648, which agrees with our calculation by number of shares. Both methods confirm that Rs. 648 is correct. Why Other Options Are Wrong: Rs. 107.04 and Rs. 648.60 do not result from any correct combination of the given values. Rs. 500 and Rs. 540 are lower than 12% of Rs. 5,400. Only Rs. 648 corresponds exactly to 12% of the correct total nominal value determined from the investment and share price. Common Pitfalls: Learners may mistakenly assume that the dividend is 12% of the investment (4,455) rather than 12% of the nominal value. Others might use Rs. 8.25 instead of Rs. 10 as the base for the 12% calculation. Always separate market price (used to determine how many shares you get) from face value (used to compute dividends). Final Answer: His annual dividend income is Rs. 648.

Question 15

Find the total cost of 96 shares of Rs. 10 each that are quoted at a discount of Re. 0.75 per share (that is, at Rs. 9.25), if brokerage is Re. 0.25 per share.

Accepted Answer

Introduction / Context: This question deals with calculating the total cost of buying a fixed number of shares when both a discount and brokerage per share are specified. Here, the shares have a face value of Rs. 10 but are available at a small discount, and a flat brokerage per share is added on top of the market price to get the effective purchase cost. Given Data / Assumptions: Number of shares = 96. Face value of each share = Rs. 10. Discount per share = Re. 0.75, so quoted market price per share = 10 - 0.75 = Rs. 9.25. Brokerage per share = Re. 0.25. We assume no other costs or taxes. Concept / Approach: The effective cost per share is the sum of the market price and the brokerage. Once we know this per-share cost, we multiply by the number of shares to find the total investment. The steps are: 1. Find quoted price after discount. 2. Add brokerage per share to obtain effective cost per share. 3. Multiply by number of shares to get total cost. Step-by-Step Solution: Step 1: Quoted market price per share = face value - discount = 10 - 0.75 = Rs. 9.25. Step 2: Brokerage per share = Re. 0.25. Step 3: Effective cost per share = 9.25 + 0.25 = Rs. 9.50. Step 4: Number of shares purchased = 96. Step 5: Total cost of 96 shares = 96 * 9.50. Step 6: Compute 96 * 9.50 = (96 * 9) + (96 * 0.5) = 864 + 48 = Rs. 912. Step 7: Therefore, the buyer must pay Rs. 912 in total to purchase these 96 shares. Verification / Alternative check: We can also reason that the total discount on face value is 96 * 0.75 = Rs. 72 and total brokerage is 96 * 0.25 = Rs. 24. If there were no discount or brokerage, cost at face value would be 96 * 10 = Rs. 960. Then apply the net adjustment: cost = 960 - 72 + 24 = 960 - 48 = Rs. 912, confirming our answer. Why Other Options Are Wrong: Rs. 921 and Rs. 920 result from incorrect arithmetic in applying discount or brokerage. Rs. 900 would mean an effective price below Rs. 9.50 per share, which contradicts the given data. Rs. 960 corresponds to purchasing at face value without discount or brokerage and therefore does not match the conditions of the problem. Only Rs. 912 correctly incorporates both the discount and the brokerage per share. Common Pitfalls: Common mistakes include ignoring brokerage or subtracting it instead of adding it in a purchase scenario. Some students also apply the discount to the total cost incorrectly rather than computing the quoted price per share first. Always work stepwise: adjust the face value to get the market price, then add brokerage, then multiply by the number of shares. Final Answer: The total cost of the 96 shares is Rs. 912.

Question 16

The cash realised on selling Rs. 100 nominal of a 14% stock is Rs. 106.25 after paying brokerage of 1/4%. What is the market value (quoted price) per Rs. 100 nominal before brokerage?

Accepted Answer

Introduction / Context: This question asks us to reverse the usual sale calculation. Instead of starting from the market price and finding the cash realised, we are given the net cash realised after brokerage and must determine the original quoted market price per Rs. 100 nominal. Brokerage is given as a percentage, and is deducted from the market value to obtain the net sale proceeds. Given Data / Assumptions: Nominal value of stock considered = Rs. 100. Cash realised after sale and brokerage = Rs. 106.25. Brokerage rate = 1/4% = 0.25% of the market value. We must find the market value before brokerage. The 14% dividend rate is not directly needed for this calculation. Concept / Approach: Let P be the market value per Rs. 100 nominal. On selling, the broker charges 0.25% of P as brokerage. Net cash realised is then: net cash = P - (0.25 / 100) * P = P * (1 - 0.0025) = P * (0.9975) We are told that this net cash equals Rs. 106.25. We solve this simple linear equation for P to get the market price before brokerage. Step-by-Step Solution: Step 1: Let P be the market value per Rs. 100 nominal. Step 2: Brokerage at 0.25% of P = (0.25 / 100) * P = 0.0025 * P. Step 3: Net cash realised = P - 0.0025 * P = P * (1 - 0.0025) = 0.9975 * P. Step 4: Given net cash realised = Rs. 106.25. Step 5: Therefore, 0.9975 * P = 106.25. Step 6: So P = 106.25 / 0.9975 ≈ Rs. 106.50. Step 7: Hence, the quoted market price per Rs. 100 nominal is approximately Rs. 106.50. Verification / Alternative check: Check by forward calculation: if market value P = Rs. 106.50, brokerage = 0.25% of 106.50 = (0.25 / 100) * 106.50 = Rs. 0.26625. Net cash realised = 106.50 - 0.26625 ≈ Rs. 106.23, which is very close to 106.25, the small difference due to rounding. Approximating brokerage to Rs. 0.25 gives net cash 106.50 - 0.25 = 106.25 exactly, which is acceptable in aptitude problems. Why Other Options Are Wrong: Rs. 100 and Rs. 105 are too low and would produce net proceeds well below Rs. 106.25 even before brokerage. Rs. 110 or Rs. 120 would produce much higher net proceeds than Rs. 106.25 given such a small brokerage rate. Rs. 106.50 is the only value that nearly exactly reproduces the net cash of Rs. 106.25 after brokerage is deducted. Common Pitfalls: A common mistake is to subtract brokerage from the nominal value or to ignore brokerage altogether. Others may attempt to apply the 14% dividend rate, which is not needed here. The key idea is that net cash is the market price minus a percentage of that market price, which leads directly to a simple equation in P. Final Answer: The market value per Rs. 100 nominal is approximately Rs. 106.50.

Question 17

Mr. Shankar spends 25% of his monthly salary on household expenditure, 20% of the remaining on children education, and invests the entire balance equally in three different schemes. If the amount invested in each scheme is Rs. 5,600, what is his mon…

Accepted Answer

Introduction / Context: This is a percentage and allocation problem involving a person's monthly salary distributed across expenses and investments. After a sequence of percentage deductions, the remaining amount is invested equally into three schemes. From the amount invested in each scheme, we must reverse the steps to compute the original monthly salary of Mr. Shankar. Given Data / Assumptions: Shankar spends 25% of his monthly salary on household expenses. He spends 20% of the remaining amount on children education. The rest is invested equally in three schemes. Amount invested in each scheme = Rs. 5,600. There are exactly three schemes, so the total invested amount is 3 * 5,600. Concept / Approach: Let the monthly salary be S. We apply the percentage expenditures stepwise and express the final balance (which is invested) in terms of S. Since we know the amount invested in each scheme, we equate the total investment with the final balance and solve for S. The idea is to work from the end (invested amount) back to the beginning (salary). Step-by-Step Solution: Step 1: Let monthly salary = S rupees. Step 2: Shankar spends 25% of S on household expenditure, so household spending = 0.25 * S. Step 3: Amount left after household expenses = S - 0.25 * S = 0.75 * S. Step 4: He spends 20% of this remaining amount on children education: 0.20 * 0.75 * S = 0.15 * S. Step 5: Amount left after children education = 0.75 * S - 0.15 * S = 0.60 * S. Step 6: This remaining 60% of S is invested equally in three schemes. Step 7: Amount invested in each scheme = Rs. 5,600, so total invested = 3 * 5,600 = Rs. 16,800. Step 8: Therefore, 0.60 * S = 16,800. Step 9: Solve for S: S = 16,800 / 0.60 = 28,000. Step 10: Hence, Shankar's monthly salary is Rs. 28,000. Verification / Alternative check: Check the distribution using S = 28,000. Household expenditure = 25% of 28,000 = 7,000. Remaining = 21,000. Children education = 20% of 21,000 = 4,200. Remaining = 16,800. This remaining amount is invested, and divided equally into three schemes each receives 16,800 / 3 = 5,600. Everything is consistent with the problem statement. Why Other Options Are Wrong: For Rs. 34,000 or Rs. 31,245, the final remaining amount after the given percentage deductions would not equal Rs. 16,800, and the per-scheme investment would differ from Rs. 5,600. Rs. 24,315 and Rs. 30,000 similarly fail to reproduce the given invested amount per scheme. Only Rs. 28,000 leads to a final investable amount of Rs. 16,800, matching all conditions. Common Pitfalls: Students often mix up the base for each percentage, incorrectly applying 20% to the original salary instead of to the remaining amount. Another common mistake is to treat the 60% remaining as 55% by subtracting 25% and 20% directly. Here the second percentage applies to the remaining money, not to the whole salary, so the final fraction is 0.75 * 0.80 = 0.60 of S. Final Answer: The monthly salary of Shankar is Rs. 28,000.

Question 18

The market value of a 10.5% stock is such that an income of Rs. 756 is obtained by investing Rs. 9,000, when brokerage is 1/4%. What is the quoted market price per Rs. 100 nominal of this stock?

Accepted Answer

Introduction / Context: This question requires working backwards from the investor's income and total outlay, taking brokerage into account, to find the market value of a 10.5% stock. The key is to determine the nominal value of stock purchased from the income, then relate the nominal value and brokerage to the total amount invested in order to solve for the market price per Rs. 100 nominal. Given Data / Assumptions: Dividend rate = 10.5% stock, so dividend per Rs. 100 nominal = Rs. 10.50. Total income from dividend = Rs. 756. Total amount invested (including brokerage) = Rs. 9,000. Brokerage rate = 1/4% = 0.25% of the market value. We must find the quoted market price P per Rs. 100 nominal. Concept / Approach: First, use the dividend rate and the total income to find the total nominal value N of stock purchased. Then, express the total amount invested as the sum of the market value of this nominal stock and the brokerage on it. With brokerage as a percentage of the market value, the total invested can be written as: total invested = market value * (1 + brokerage rate) This relationship allows us to solve for the market value and then for the price per Rs. 100 nominal. Step-by-Step Solution: Step 1: Let N be the total nominal value of stock purchased. Step 2: Dividend at 10.5% on N = 0.105 * N. Step 3: Given this equals Rs. 756, so 0.105 * N = 756. Step 4: Solve for N: N = 756 / 0.105 = Rs. 7,200 nominal. Step 5: Let P be the market price per Rs. 100 nominal. Then market value of N nominal = (N / 100) * P = 72 * P. Step 6: Brokerage at 0.25% of market value = 0.0025 * (72 * P) = 0.18 * P. Step 7: Total invested (including brokerage) = market value + brokerage = 72 * P + 0.18 * P = 72.18 * P. Step 8: Given total invested = Rs. 9,000, so 72.18 * P = 9,000. Step 9: Solve for P: P = 9000 / 72.18 ≈ Rs. 124.75. Step 10: Therefore, the quoted market price is approximately Rs. 124.75 per Rs. 100 nominal. Verification / Alternative check: Using P ≈ 124.75, market value of 7,200 nominal = 72 * 124.75 = Rs. 8,982. Brokerage at 0.25% ≈ 0.0025 * 8,982 ≈ Rs. 22.46. Total cost ≈ 8,982 + 22.46 ≈ Rs. 9,004.46, which is acceptably close to Rs. 9,000 considering rounding. In many aptitude texts, this is rounded to match Rs. 9,000 with P taken as exactly 124.75. Why Other Options Are Wrong: Values like Rs. 108.25 or Rs. 112.20 produce total costs and income combinations that do not match the given 9,000 investment and 756 income. Rs. 125.25 similarly leads to inconsistent totals. Rs. 120 gives an income lower than Rs. 756 for a 9,000 outlay. Only Rs. 124.75 satisfies all given conditions within normal rounding limits. Common Pitfalls: A common error is to ignore brokerage, treating 9,000 as pure market value and getting too low a market price. Others mistakenly compute dividend on the amount invested instead of on the nominal value. The correct approach always involves finding nominal value from income using the dividend rate and then relating nominal value and brokerage to the invested amount. Final Answer: The market value of the 10.5% stock is approximately Rs. 124.75 per Rs. 100 nominal.

Question 19

A man invests some money partly in 9% stock at Rs. 96 and partly in 12% stock at Rs. 120, and he receives equal dividends from both. In what ratio must he invest in the two stocks to make the dividends equal?

Accepted Answer

Introduction / Context: This question is about dividing an investment between two different stocks such that the dividend income from each stock is the same. The two stocks have different dividend rates and different market prices, so the amount invested in each must be carefully chosen to equalise the annual income from them. Given Data / Assumptions: First stock: 9% stock at Rs. 96 per Rs. 100 nominal. Second stock: 12% stock at Rs. 120 per Rs. 100 nominal. Dividend is calculated on nominal value, while investment is made at the market price. Dividends received from both investments must be equal. Concept / Approach: Let the money invested in the 9% stock be x rupees and the money invested in the 12% stock be y rupees. We compute the dividend from each in terms of x and y, then set these dividends equal. This yields an equation that gives the ratio x : y. Income from each stock is found by converting investment to nominal value and then applying the dividend rate. Step-by-Step Solution: Step 1: For the 9% stock at Rs. 96, nominal value bought with x rupees = (x / 96) * 100. Step 2: Dividend from this nominal value at 9% = 9% of (x / 96 * 100) = (9 / 100) * (x / 96 * 100) = 9x / 96. Step 3: For the 12% stock at Rs. 120, nominal value bought with y rupees = (y / 120) * 100. Step 4: Dividend from this nominal value at 12% = 12% of (y / 120 * 100) = 12y / 120 = y / 10. Step 5: We are told that dividends from both investments are equal, so: 9x / 96 = y / 10. Step 6: Cross multiply: 9x * 10 = 96y, so 90x = 96y. Step 7: Divide both sides by 6 to simplify: 15x = 16y. Step 8: Therefore, x / y = 16 / 15, so the required investment ratio is 16 : 15. Verification / Alternative check: Assume we invest 16,000 rupees in the 9% stock and 15,000 rupees in the 12% stock. The nominal value for the first stock is (16000 / 96) * 100 ≈ 16,666.67, giving dividend ≈ 0.09 * 16666.67 ≈ 1,500. For the second stock, nominal value = (15000 / 120) * 100 = 12,500, dividend = 0.12 * 12500 = 1,500. The dividends are equal, confirming the ratio 16 : 15. Why Other Options Are Wrong: Ratios such as 3 : 5, 2 : 1, 4 : 5, or 5 : 4 do not produce equal dividends when used as x : y in the calculations above. Only 16 : 15 ensures that the dividend from the 9% stock matches the dividend from the 12% stock for any common multiple of investments. Common Pitfalls: A typical mistake is to compare only the percentages 9% and 12% and ignore the differing market prices. Some learners also incorrectly take the ratio of dividend rates to decide the investment split. The correct method is to equate the actual dividend amounts derived from the investments, which involves both dividend rates and market prices. Final Answer: To obtain equal dividends from both stocks, the investor must invest in the ratio 16 : 15 in 9% stock at Rs. 96 and 12% stock at Rs. 120.

Question 20

An investor A buys a 10% stock at Rs. 96 per Rs. 100 nominal. If investor B wants to invest in a 12% stock that is equally good in terms of yield, at what market price per Rs. 100 nominal should B buy the 12% stock?

Accepted Answer

Introduction / Context: This question asks us to determine the price at which a 12% stock should be bought so that it provides the same yield as another investment in a 10% stock at a known price. It is an application of the idea that two investments are "equally good" when they offer the same percentage return on the money invested, even if their nominal rates and market prices differ. Given Data / Assumptions: First investment: 10% stock at Rs. 96 per Rs. 100 nominal. Second investment: 12% stock at an unknown market price P per Rs. 100 nominal. We want both investments to yield the same percentage return. No brokerage is mentioned. Concept / Approach: Yield on investment is computed as: yield % = (dividend per share / market price per share) * 100 For the two investments to be equally good, their yields must be equal. We compute the yield from the 10% stock at Rs. 96, then set this equal to the yield from the 12% stock at price P and solve for P. Step-by-Step Solution: Step 1: For the 10% stock, dividend per Rs. 100 nominal = 10% of 100 = Rs. 10. Step 2: Market price for this stock = Rs. 96. Step 3: Yield from this investment = (10 / 96) * 100 ≈ 10.4167%. Step 4: For the 12% stock, dividend per Rs. 100 nominal = 12% of 100 = Rs. 12. Step 5: Let P be the market price per Rs. 100 nominal for the 12% stock. Step 6: Yield from the 12% stock = (12 / P) * 100. Step 7: Set yields equal: (12 / P) * 100 = (10 / 96) * 100. Step 8: Simplify: 12 / P = 10 / 96. Step 9: Cross multiply: 12 * 96 = 10 * P. Step 10: Compute 12 * 96 = 1,152, so P = 1,152 / 10 = Rs. 115.20. Verification / Alternative check: Check yields: For 10% stock at 96, yield ≈ 10.4167%. For 12% stock at 115.20, yield = (12 / 115.20) * 100 = (0.1041667) * 100 ≈ 10.4167%. Since both give the same percentage return, they are equally good investments at these respective prices. Why Other Options Are Wrong: Rs. 80 would produce a higher yield than the 10% stock at 96, making it better, not equal. Rs. 120 and Rs. 125.40 would produce lower yields and thus be inferior. Rs. 96 would make the 12% stock clearly better than the 10% stock at 96. Only Rs. 115.20 ensures equality of yields. Common Pitfalls: Some students erroneously match only the percentages 10% and 12% without considering price, or they equate 10% of 96 with 12% of P incorrectly. Always base yield on dividend per Rs. 100 nominal divided by the market price, and then equate the two yields carefully to find the unknown price. Final Answer: B must purchase the 12% stock at a market price of Rs. 115.20 per Rs. 100 nominal to make it equally good as the 10% stock at Rs. 96.

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