Question 1

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 is effectively the same numerical situation as a previous question, again testing how to compute the market value of a stock given the total income, total investment, and brokerage. It reinforces the procedure of first finding the nominal value from the income and dividend rate, and then incorporating brokerage to determine the market price. Given Data / Assumptions: Dividend rate = 10.5% stock, so dividend on Rs. 100 nominal = Rs. 10.50. Total dividend income = 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 per Rs. 100 nominal. Concept / Approach: As before, we first determine the total nominal value N of the stock from the relation dividend = 0.105 * N. Then if P is the market price per Rs. 100 nominal, the market value is (N / 100) * P and brokerage is 0.25% of this market value. The total investment is market value plus brokerage. Setting this equal to Rs. 9,000 allows us to solve for P. Step-by-Step Solution: Step 1: Let N be the nominal value of stock purchased. Step 2: Dividend at 10.5% on N is 0.105 * N. Step 3: Given income = Rs. 756, so 0.105 * N = 756. Step 4: Solve: N = 756 / 0.105 = Rs. 7,200 nominal. Step 5: Let P be the market price per Rs. 100 nominal. Step 6: Market value of stock = (7200 / 100) * P = 72 * P. Step 7: Brokerage = 0.25% of market value = 0.0025 * 72 * P = 0.18 * P. Step 8: Total investment = market value + brokerage = 72 * P + 0.18 * P = 72.18 * P. Step 9: Given total investment = 9,000, so 72.18 * P = 9,000. Step 10: P = 9000 / 72.18 ≈ Rs. 124.75. Verification / Alternative check: As before, use P ≈ 124.75. Market value ≈ 72 * 124.75 = Rs. 8,982 and brokerage ≈ 0.25% of 8,982 ≈ Rs. 22.46. The total ≈ Rs. 9,004.46, which is close to Rs. 9,000, and rounding the price to 124.75 matches the standard answer key used in aptitude questions. Why Other Options Are Wrong: The other prices either make the total investment significantly different from Rs. 9,000 or produce a dividend income that does not match Rs. 756. For example, at Rs. 120 the income from Rs. 9,000 invested would be lower, and at Rs. 125.25 or Rs. 108.25 the income would not align with the given data. Only Rs. 124.75 fits the conditions with reasonable rounding. Common Pitfalls: The main pitfalls are ignoring brokerage or applying the dividend rate to the invested amount instead of to the nominal value. Some also forget to treat brokerage as an extra percentage cost on the market value, leading to an underestimated market price. Following the structured method avoids these issues. Final Answer: The market value of the 10.5% stock is approximately Rs. 124.75 per Rs. 100 nominal.

Question 2

A man buys shares of face value Rs. 25 each in a company that pays a 9% dividend. If his investment is such that it yields 10% on the money he puts in, at what price per share did he buy the shares?

Accepted Answer

Introduction / Context: This problem asks for the purchase price of a share, given its face value, the declared dividend rate on face value, and the effective yield that the investor actually earns on his investment. It illustrates how the purchase price affects the relationship between the nominal dividend rate and the actual return on the investor's money. Given Data / Assumptions: Face value of each share = Rs. 25. Dividend rate = 9% on face value. Yield on the investor's money = 10%. We must find the market price P at which the shares are purchased. No brokerage is mentioned. Concept / Approach: First compute the annual dividend per share using the face value and dividend rate. Then apply the yield formula to find the purchase price. Yield on investment is defined as: yield % = (annual dividend per share / purchase price per share) * 100 We set this yield equal to 10% and solve for the unknown purchase price P. Step-by-Step Solution: Step 1: Face value of the share = Rs. 25. Step 2: Dividend rate = 9%. Step 3: Annual dividend per share = 9% of 25 = (9 / 100) * 25 = Rs. 2.25. Step 4: Let P be the purchase price per share. Step 5: Yield on investment is 10%, so (2.25 / P) * 100 = 10. Step 6: Simplify: 2.25 / P = 10 / 100 = 0.10. Step 7: Solve for P: P = 2.25 / 0.10 = Rs. 22.50. Step 8: Therefore, the man bought the shares at Rs. 22.50 each. Verification / Alternative check: Check the yield explicitly: if the share costs Rs. 22.50 and pays a dividend of Rs. 2.25 per year, then yield % = (2.25 / 22.50) * 100 = 0.10 * 100 = 10%. This matches the given yield, confirming that Rs. 22.50 is the correct purchase price. Why Other Options Are Wrong: At Rs. 22, the yield would be (2.25 / 22) * 100, which is slightly above 10%. At Rs. 20.45, the yield is even higher. At Rs. 12.50, the yield would be extremely high, far more than 10%. Purchasing at Rs. 25 (face value) would produce a yield of only (2.25 / 25) * 100 = 9%, equal to the dividend rate but less than the desired 10%. Only Rs. 22.50 produces the exact 10% return. Common Pitfalls: Some students mistakenly treat 9% as the yield and ignore the 10% figure, or they try to average the two percentages. Others forget to divide dividend by price when calculating yield and instead subtract percentages. Always use the yield formula with the correct base: yield depends on the purchase price, not on the face value. Final Answer: He bought the shares at a price of Rs. 22.50 per share.

Question 3

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

Accepted Answer

Introduction / Context: In questions on stocks and shares, one of the most common skills tested is the relation between investment, market price, nominal value and dividend percentage. This problem asks for the dividend rate, given how much money is invested, the quoted price of the stock, and the annual income received. Understanding how to convert an investment at a quoted price into nominal value is essential for aptitude and banking exams. Given Data / Assumptions: Total investment = Rs 1552 Market price of Rs 100 nominal stock = Rs 97 (stock quoted at 97) Annual income (dividend received) = Rs 128 Dividend is paid on nominal (face) value, not on the market price Concept / Approach: The key idea is that when stock is quoted at 97, it means a Rs 100 nominal share costs Rs 97 in the market. First we find the total nominal value of stock purchased using investment and market price. Then we apply the standard formula: Dividend rate (%) = (Annual income / Nominal value) * 100. This gives the required percentage return declared by the company on the face value. Step-by-Step Solution: Step 1: Market price of Rs 100 nominal stock = Rs 97. Step 2: Nominal value purchased = (Investment / Market price) * 100. Step 3: Nominal value = (1552 / 97) * 100 = 1600. Step 4: Dividend is paid on nominal value, so annual dividend = 128. Step 5: Dividend rate (%) = (128 / 1600) * 100 = 8%. Verification / Alternative check: If the dividend rate is 8%, then dividend on Rs 1600 nominal value is 1600 * 8 / 100 = Rs 128, which matches the given income. This confirms that the computed rate is consistent with the information provided. Why Other Options Are Wrong: 8.5%: This would give income 1600 * 8.5 / 100 = Rs 136, which is higher than Rs 128. 7.5%: This would give income 1600 * 7.5 / 100 = Rs 120, which is less than Rs 128. 9%: This would give income 1600 * 9 / 100 = Rs 144, which does not match the given income. Common Pitfalls: Using the market value instead of nominal value to compute dividend. Confusing the quoted price 97 with 97% dividend, which is incorrect. Forgetting to multiply by 100 when converting the fraction to a percentage. Final Answer: The correct dividend rate of the stock is 8%.

Question 4

Find the cost price of Rs 4500 nominal value of 8.5 percent stock purchased at 4 percent premium in the market.

Accepted Answer

Introduction / Context: This question checks your understanding of how to calculate the market cost of buying a given nominal amount of stock when the stock is quoted at a premium. In stock and share problems, nominal value, premium or discount, and percentage dividend are standard concepts, but here we focus only on the cost of purchase when the market price is above face value. Given Data / Assumptions: Nominal value of stock required = Rs 4500 Stock pays 8.5 percent dividend (not directly used in this cost calculation) Stock is purchased at 4 percent premium Face value (nominal value) is assumed to be Rs 100 per share unless otherwise stated Concept / Approach: When a stock is at 4 percent premium, it means a Rs 100 nominal share costs Rs 104 in the market. The cost of any given nominal value is found by scaling this price. Formula: Cost price = Nominal value * (Market price per 100 nominal / 100). So we multiply the total nominal value by 104 and divide by 100. Step-by-Step Solution: Step 1: Market price of Rs 100 nominal stock at 4 percent premium = Rs 104. Step 2: Total nominal value required = Rs 4500. Step 3: Cost price = 4500 * 104 / 100. Step 4: Simplify: 4500 * 104 / 100 = 45 * 104 = 4680. Step 5: Therefore the investor must pay Rs 4680 to buy Rs 4500 nominal value of stock. Verification / Alternative check: A quick check is to note that the premium is 4 percent on Rs 4500, which is 0.04 * 4500 = Rs 180. Adding this to the nominal value 4500 gives 4500 + 180 = Rs 4680, which matches the detailed calculation. This alternative view reinforces the correctness of the result. Why Other Options Are Wrong: Rs 1400: Far too small; it ignores both nominal value and premium. Rs 5000: This would correspond to a much higher effective premium than 4 percent. Rs 4000: This is less than the nominal value and would represent a discount, not a premium. Common Pitfalls: Using 4 percent of the market value instead of the nominal value. Interpreting 4 premium as Rs 4 rather than 4 percent on Rs 100 nominal. Confusing dividend percentage with premium percentage when only cost is asked. Final Answer: The total cost of purchasing the stock is Rs 4680.

Question 5

A 14 percent stock is sold at Rs 106.25 per Rs 100 nominal share, and brokerage is charged at 3/4 percent on the selling price. What is the net cash realised per Rs 100 nominal share?

Accepted Answer

Introduction / Context: Many stock market aptitude questions involve brokerage or commission charged on buying or selling shares. This question asks for the net cash realised after selling a 14 percent stock at a certain market price when brokerage is deducted as a percentage of the selling price. The task is to find how much money the seller actually receives per Rs 100 nominal share after paying brokerage. Given Data / Assumptions: Type of stock: 14 percent stock (dividend rate is not directly required here) Selling price per Rs 100 nominal share = Rs 106.25 Brokerage rate = 3/4 percent on the selling price We must find net cash realised per Rs 100 nominal share after brokerage deduction Concept / Approach: Brokerage is a fee charged as a percentage of the selling price. Net cash realised equals the selling price minus brokerage. If brokerage rate is b percent and selling price is S, then Net cash = S * (1 - b / 100). Here, b = 0.75 and S = 106.25, so we simply apply this formula. Step-by-Step Solution: Step 1: Selling price per Rs 100 nominal share S = Rs 106.25. Step 2: Brokerage rate b = 3/4 percent = 0.75 percent. Step 3: Brokerage amount per share = S * b / 100 = 106.25 * 0.75 / 100. Step 4: 106.25 * 0.75 / 100 = 106.25 * 0.0075 = 0.796875, which is about Rs 0.80. Step 5: Net cash realised per share = 106.25 - 0.80 = Rs 105.45, which rounds to approximately Rs 105.50. Verification / Alternative check: Instead of working with decimals, observe that 0.75 percent of 100 is 0.75. Since the price is near 100, the brokerage should be slightly more than 0.75, close to 0.8. Subtracting about 0.8 from 106.25 gives around 105.45. Among the options, Rs 105.50 is the closest correct rounded value, confirming our choice. Why Other Options Are Wrong: Rs 106.00: This assumes a smaller brokerage or an incorrect percentage calculation. Rs 106.50: This is greater than the market price and ignores brokerage deduction. Rs 113.75: This value is unrelated to the given data and much higher than the selling price. Common Pitfalls: Forgetting to subtract brokerage from the selling price. Applying brokerage on nominal value instead of on the market selling price. Misinterpreting 3/4 percent as 4 percent or 3 percent. Final Answer: The net cash realised per Rs 100 nominal share is approximately Rs 105.50.

Question 6

A man buys 20 shares of Rs 50 each at Rs 5 discount per share. The company declares a dividend of 13.5 percent on the nominal value. What effective rate of interest does he obtain on his investment?

Accepted Answer

Introduction / Context: This question is a classic stocks and shares problem that tests your ability to relate nominal value, market price, discount, dividend rate and effective yield. The idea is to compute the return on the actual money invested, not on the face value. Such questions are very common in banking, SSC and other competitive exams under the topic of stocks and shares. Given Data / Assumptions: Number of shares purchased = 20 Nominal value (face value) of each share = Rs 50 Shares bought at Rs 5 discount, so market price per share = Rs 50 - Rs 5 = Rs 45 Dividend declared = 13.5 percent (13.5 percent of nominal value) We need the effective rate of interest on the investment. Concept / Approach: Dividend is always calculated on nominal value, but the investor actually pays the market price. So we first compute: Total nominal value = Number of shares * Nominal value per share. Total dividend = Dividend rate * Total nominal value. Total investment = Number of shares * Market price per share. Then effective rate of interest (or yield) is: Yield (%) = (Annual dividend / Investment) * 100. Step-by-Step Solution: Step 1: Nominal value per share = Rs 50. Step 2: Market price per share = Rs 50 - Rs 5 = Rs 45. Step 3: Total nominal value = 20 * 50 = Rs 1000. Step 4: Dividend rate = 13.5 percent, so annual dividend = 1000 * 13.5 / 100 = Rs 135. Step 5: Total investment = 20 * 45 = Rs 900. Step 6: Yield (%) = 135 / 900 * 100 = 15%. Verification / Alternative check: We can reduce the fraction 135 / 900. Divide numerator and denominator by 45: 135 / 900 = 3 / 20. Then 3 / 20 * 100 = 15%. This confirms that the effective rate of return is exactly 15 percent on the amount invested, so the chosen option is consistent. Why Other Options Are Wrong: 13%: Slightly lower than the correct yield because it ignores the effect of buying at a discount. 12%: Too low; it may come from using an incorrect dividend or investment figure. 16%: Slightly higher than the correct yield and does not match the precise calculation. Common Pitfalls: Calculating dividend on the market price instead of on nominal value. Forgetting that discount reduces cost, which increases effective yield. Incorrectly computing percentage by forgetting to multiply by 100. Final Answer: The effective rate of interest obtained on the investment is 15%.

Question 7

A 6 percent stock yields 8 percent to an investor. What is the market value of this stock per Rs 100 nominal value?

Accepted Answer

Introduction / Context: This problem tests your understanding of how market value, dividend rate and yield are related for stocks. A 6 percent stock means that the company pays Rs 6 every year on a Rs 100 nominal share. The investor, however, experiences an 8 percent return on the actual amount invested, known as the yield. We must find the market price that produces this yield. Given Data / Assumptions: Dividend rate = 6 percent on nominal value. Nominal value per share = Rs 100. Investor yield (return on investment) = 8 percent. We need the market value (price paid) per Rs 100 nominal share. Concept / Approach: Dividend received on one share is fixed by the nominal rate. Yield is defined as: Yield (%) = (Annual dividend / Market price) * 100. Rearranging this gives the formula for market price: Market price = (Annual dividend * 100) / Yield percentage. We simply substitute the given values for dividend and yield. Step-by-Step Solution: Step 1: Dividend on Rs 100 nominal value at 6 percent = 6 rupees per share. Step 2: Let M be the market value per share. Step 3: Yield (%) = (Dividend / Market value) * 100. Step 4: Given yield = 8 percent, so 8 = (6 / M) * 100. Step 5: Rearrange: M = (6 * 100) / 8 = 600 / 8 = Rs 75. Verification / Alternative check: Quickly check: If the market value is Rs 75 and the dividend is Rs 6, then the return is 6 / 75 = 0.08. Multiplying by 100 gives 8 percent, matching the stated yield. This confirms that the market value of Rs 75 is consistent with the given data and formula. Why Other Options Are Wrong: Rs 70: This would give yield = 6 / 70 * 100 which is greater than 8 percent. Rs 76: This gives a yield slightly below 8 percent. Rs 80: This would give yield = 6 / 80 * 100 = 7.5 percent, which is not correct. Common Pitfalls: Using yield as 6 percent and dividend as 8 percent, reversing the given roles. Forgetting to multiply dividend by 100 when solving for market value. Confusing nominal value with market price and using 100 instead of the unknown M in the denominator. Final Answer: The market value of the stock per Rs 100 nominal value is Rs 75.

Question 8

Find the total cost of purchasing Rs 6400 nominal value of 10 percent stock quoted at 15 percent discount in the market.

Accepted Answer

Introduction / Context: This is another important stocks and shares question where you are asked to calculate the total cost of buying a given nominal amount of stock when it is available at a discount. A discount means that the market price is lower than the nominal (face) value, and this directly reduces the investment needed for a fixed nominal amount. Given Data / Assumptions: Nominal value of stock to be purchased = Rs 6400 Dividend rate = 10 percent (not necessary for cost calculation) Stock is quoted at 15 percent discount Nominal value per share is assumed to be Rs 100 Concept / Approach: A 15 percent discount on a Rs 100 nominal share means the market price per share is 100 - 15 = Rs 85. To find the cost of Rs 6400 nominal value, we scale the price accordingly. The basic relation is: Cost price = Nominal value * (Market price per 100 nominal / 100). This converts nominal value into actual money paid with discount applied. Step-by-Step Solution: Step 1: Discount = 15 percent, so market price of Rs 100 nominal stock = 100 - 15 = Rs 85. Step 2: Total nominal value required = Rs 6400. Step 3: Cost price = 6400 * 85 / 100. Step 4: 6400 * 85 / 100 = 64 * 85 = 5440. Step 5: Therefore cost of Rs 6400 nominal 10 percent stock at 15 percent discount is Rs 5440. Verification / Alternative check: We can also think in terms of per share. If nominal value per share is Rs 100, number of shares corresponding to Rs 6400 nominal value is 6400 / 100 = 64 shares. Each share costs Rs 85 in the market. Therefore investment = 64 * 85 = 5440, which confirms the previous calculation. Why Other Options Are Wrong: Rs 2000: This is far too low and ignores the actual nominal value. Rs 6000: This would correspond to a smaller discount than 15 percent. Rs 5140: This appears random and does not equal 64 * 85. Common Pitfalls: Applying 15 percent discount on 6400 incorrectly as 6400 - 15 instead of 15 percent of 6400. Confusing discount with premium and adding instead of subtracting. Dividing instead of multiplying when converting nominal value to cost. Final Answer: The total cost of the investment is Rs 5440.

Question 9

Find the annual income obtained from investing Rs 2500 nominal value in 8 percent stock that is quoted at Rs 106 in the market.

Accepted Answer

Introduction / Context: This problem focuses on the difference between nominal value, market price and annual income from a stock. The stock pays a fixed percentage dividend on nominal value, and that dividend does not change with the quoted market price. The question asks only for annual income, so we do not need to use the market quotation except to understand the context. Given Data / Assumptions: Nominal value of stock purchased = Rs 2500 Dividend rate = 8 percent per year Market price (quoted) = Rs 106 per Rs 100 nominal value Dividend is always calculated on nominal value Concept / Approach: The dividend formula for a stock investment is simple: Annual dividend (income) = Nominal value * Dividend rate / 100. Here only nominal value and rate matter. The fact that the stock is at 106 means the investor would have paid more than nominal value, but that affects yield, not the absolute dividend amount. Since the question is about annual income, we ignore market price in the calculation. Step-by-Step Solution: Step 1: Total nominal value of holdings = Rs 2500. Step 2: Dividend rate = 8 percent per year. Step 3: Annual income = 2500 * 8 / 100. Step 4: 2500 * 8 / 100 = 25 * 8 = Rs 200. Step 5: Therefore the investor receives Rs 200 as annual dividend. Verification / Alternative check: Think per Rs 100 nominal. At 8 percent, every Rs 100 nominal share pays Rs 8 per year. For Rs 2500 nominal value, the number of Rs 100 blocks is 2500 / 100 = 25. Income = 25 * 8 = Rs 200, which matches the earlier computation, confirming the result. Why Other Options Are Wrong: Rs 100: This would correspond to a 4 percent dividend rate, not 8 percent. Rs 150: Does not match 8 percent of 2500 and may come from a mistake in multiplication. Rs 250: This would match a 10 percent rate rather than the given 8 percent. Common Pitfalls: Mistakenly using the market price 106 in the dividend calculation. Computing 8 percent of 250 instead of 2500 due to a missing zero. Confusing yield on investment with absolute dividend income. Final Answer: The annual income derived from the investment is Rs 200.

Question 10

Find the annual income obtained by investing Rs 6800 in 10 percent stock that is quoted at Rs 136 per Rs 100 nominal share.

Accepted Answer

Introduction / Context: This question combines the idea of investment at a quoted market price with calculation of annual dividend income from a percentage stock. Although the investor is told how much money is invested and at what price the stock is quoted, the dividend itself is always computed on the nominal value of the shares, not on the amount invested. Given Data / Assumptions: Total money invested = Rs 6800 Market price of Rs 100 nominal stock = Rs 136 Dividend rate on nominal value = 10 percent per year We must find the annual income (dividend) from this investment Concept / Approach: First step is to convert the investment and market price into nominal value of stock purchased. If a Rs 100 nominal share costs Rs 136, each rupee of nominal value costs 136 / 100 rupees. Once we know the total nominal value, we apply: Annual dividend = Nominal value * Dividend rate / 100. Step-by-Step Solution: Step 1: Market price of Rs 100 nominal stock = Rs 136. Step 2: Let N be the total nominal value purchased. Then 6800 = N * 136 / 100. Step 3: Rearranging, N = 6800 * 100 / 136. Step 4: N = 6800 / 136 * 100 = 50 * 100 = Rs 5000 nominal value. Step 5: Dividend rate = 10 percent, so annual income = 5000 * 10 / 100 = Rs 500. Verification / Alternative check: Check in a more intuitive way. Price per Rs 100 nominal is 136. Investment 6800 divided by 136 gives the number of Rs 100 shares: 6800 / 136 = 50 shares of Rs 100 nominal each. So nominal value = 50 * 100 = 5000. Dividend at 10 percent is Rs 10 per share, hence 50 * 10 = Rs 500, confirming the previous calculation. Why Other Options Are Wrong: Rs 250: Corresponds to a 5 percent dividend on Rs 5000 nominal value. Rs 1500: Too large; this would imply a 30 percent dividend rate, which is not given. Rs 50: Too low; this would represent only 1 percent on Rs 5000 nominal value. Common Pitfalls: Using the investment 6800 directly with the 10 percent rate instead of converting to nominal value. Incorrectly computing the nominal value by dividing by 1.36 instead of 136 / 100. Forgetting the 100 factor when moving between per rupee and per Rs 100 nominal values. Final Answer: The annual income derived from the investment is Rs 500.

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