Samacheer Kalvi Class 11 Business Maths Solutions Chapter 7 Financial Mathematics Exercise 7.2

Question 1. Find the market value of 62 shares available at Rs. 132 having the par value of Rs. 100.
Answer: To find the market value of shares, we multiply the number of shares by the market value of each share. The par value (face value) of the shares is given as Rs. 100, but for calculating the market value, we use the price at which the shares are currently available, which is Rs. 132.
Market Value \( = \) Number of shares \( \times \) Market value per share
Market Value \( = \text{Rs. } 132 \times 62 \)
Market Value \( = \text{Rs. } 8,184 \)
In simple words: We multiply the number of shares by how much each share costs in the market to find the total market value.

🎯 Exam Tip: Remember to always use the market value of the share for calculating the total market value, not the par value, unless the shares are issued or traded at par.

Question 2. How much will be required to buy 125 of Rs. 25 shares at a discount of Rs. 7.
Answer: First, we need to find the market value of one share. Since the shares are at a discount, we subtract the discount from the face value. Then, we multiply this market value by the number of shares to find the total amount needed.
Face value of a share \( = \text{Rs. } 25 \)
Discount \( = \text{Rs. } 7 \)
Market value of a share \( = \text{Rs. } 25 - \text{Rs. } 7 = \text{Rs. } 18 \)
Amount required to buy 125 shares \( = \) Number of shares \( \times \) Market value of a share
Amount required \( = 125 \times \text{Rs. } 18 \)
Amount required \( = \text{Rs. } 2,250 \)
In simple words: We first subtract the discount from the face value to get the current price of one share. Then, we multiply this price by the total number of shares to find the full amount needed.

🎯 Exam Tip: Always calculate the actual market price of one share first, especially when there is a premium or discount, before multiplying by the total number of shares.

Question 3. If the dividend received from 9% of Rs. 20 shares is Rs. 1,620, find the number of shares.
Answer: We can find the number of shares by using the formula for income from dividends. The income is calculated based on the face value of the shares and the dividend rate. We are given the total income, so we can work backward to find the number of shares.
Income \( = \) Number of shares \( \times \) Face value of a share \( \times \) Rate of dividend
We are given: Income \( = \text{Rs. } 1,620 \)
Face value of a share \( = \text{Rs. } 20 \)
Rate of dividend \( = 9\% = \frac{9}{100} \)
So, \( 1,620 = \text{Number of shares} \times \text{Rs. } 20 \times \frac{9}{100} \)
Now, we solve for the Number of shares:
Number of shares \( = \frac{1620 \times 100}{20 \times 9} \)
Number of shares \( = \frac{162000}{180} \)
Number of shares \( = 900 \)
In simple words: If we know how much money someone got from dividends, and we know the dividend rate and the face value of each share, we can figure out how many shares they own.

🎯 Exam Tip: When calculating income from shares, remember that the dividend rate is always applied to the face value of the shares, not their market value.

Question 4. Mohan invested Rs. 29,040 in 15% of Rs. 100 shares of a company quoted at a premium of 20%. Calculate
(i) the number of shares bought by Mohan
(ii) his annual income from shares
(iii) the percentage return on his investment
Answer: Mohan's investment details are: Investment \( = \text{Rs. } 29,040 \), Rate of dividend \( = 15\% \), Face value of each share \( = \text{Rs. } 100 \), Premium \( = 20\% \).
(i) To find the number of shares, we first need to calculate the market value of one share. Since the shares are at a premium of 20%, the market value is the face value plus 20% of the face value.
Market value of a share \( = \text{Face value} + \text{Premium} \)
Market value of a share \( = \text{Rs. } 100 + (20\% \text{ of Rs. } 100) = \text{Rs. } 100 + \text{Rs. } 20 = \text{Rs. } 120 \)
Now, Number of shares \( = \frac{\text{Investment}}{\text{Market value of a share}} \)
Number of shares \( = \frac{\text{Rs. } 29,040}{\text{Rs. } 120} = 242 \)
(ii) To find the annual income, we multiply the number of shares, the face value of each share, and the rate of dividend.
Annual income from shares \( = \) Number of shares \( \times \) Face value of a share \( \times \) Rate of dividend
Annual income \( = 242 \times \text{Rs. } 100 \times \frac{15}{100} \)
Annual income \( = 242 \times 15 = \text{Rs. } 3,630 \)
(iii) The percentage return on investment is found by dividing the annual income by the total investment and multiplying by 100.
Percentage return on investment \( = \frac{\text{Income}}{\text{Investment}} \times 100 \)
Percentage return \( = \frac{\text{Rs. } 3,630}{\text{Rs. } 29,040} \times 100 \)
Percentage return \( = \frac{363}{2904} \times 100 = \frac{1}{8} \times 100 = 12.5\% \)
Which can also be written as \( 12\frac{1}{2}\% \). This shows how efficient an investment is.
In simple words: First, find the real price of one share (market value). Then, see how many shares were bought. Next, calculate the yearly earnings from these shares. Finally, work out the percentage profit on the money put in.

🎯 Exam Tip: When calculating market value, remember that a 'premium' adds to the face value, while a 'discount' subtracts from it.

Question 5. A man buys 400 of Rs. 10 shares at a premium of Rs. 2.50 on each share. If the rate of dividend is 12% find
(i) his investment
(ii) annual dividend received by him
(iii) rate of interest received by him on his money
Answer: We are given: Number of shares \( = 400 \), Face value of a share \( = \text{Rs. } 10 \), Premium \( = \text{Rs. } 2.50 \), Rate of dividend \( = 12\% \).
First, calculate the market value of one share:
Market value of a share \( = \text{Face value} + \text{Premium} \)
Market value of a share \( = \text{Rs. } 10 + \text{Rs. } 2.50 = \text{Rs. } 12.50 \)
(i) To find the total investment, multiply the number of shares by their market value.
Investment \( = \) Number of shares \( \times \) Market value of a share
Investment \( = 400 \times \text{Rs. } 12.50 = \text{Rs. } 5,000 \)
(ii) To find the annual dividend, multiply the number of shares, their face value, and the dividend rate. Dividends are always calculated on the face value.
Annual dividend \( = \) Number of shares \( \times \) Face value \( \times \) Rate of dividend
Annual dividend \( = 400 \times \text{Rs. } 10 \times \frac{12}{100} \)
Annual dividend \( = 400 \times 10 \times 0.12 = \text{Rs. } 480 \)
(iii) The rate of interest (or return) on his money is the dividend received divided by the total investment, expressed as a percentage.
Rate of interest \( = \frac{\text{Annual dividend}}{\text{Investment}} \times 100 \)
Rate of interest \( = \frac{\text{Rs. } 480}{\text{Rs. } 5,000} \times 100 \)
Rate of interest \( = \frac{48000}{5000} = \frac{48}{5} = 9.6\% \)
This percentage shows the actual return the investor gets on the money they put in.
In simple words: First, find the total money put in. Then, calculate the total money earned from dividends. Finally, see what percentage of the invested money was earned back each year.

🎯 Exam Tip: Always distinguish between face value (used for calculating dividends) and market value (used for calculating total investment or sale proceeds).

Question 6. Sundar bought 4,500 of Rs. 10 shares, paying 2% per annum. He sold them when the price rose to Rs. 23 and invested the proceeds in 25 shares paying 10% per annum at Rs. 18. Find the change in his income.
Answer: We need to calculate Sundar's income before selling the shares and his income after reinvesting. The difference between these two incomes will be the change.
**First Scenario: Original Investment**
Number of shares \( = 4,500 \)
Face value of each share \( = \text{Rs. } 10 \)
Dividend rate \( = 2\% \)
Initial income \( = \) Number of shares \( \times \) Face value \( \times \) Dividend rate
Initial income \( = \frac{4500}{10} \times \text{Rs. } 10 \times \frac{2}{100} \) (This step calculates how many Rs. 10 shares he has if 4500 is the total face value amount; if 4500 is the number of shares then it would be \( 4500 \times 10 \times \frac{2}{100} \). The source shows \( \frac{4500}{10} \), implying 4500 is the total value of shares, not the number of shares. Let's proceed with the source's calculation interpretation.)
Initial Number of shares \( = \frac{\text{Total Face Value}}{\text{Face Value per share}} = \frac{4500}{10} = 450 \text{ shares} \)
Income from 2% stock \( = 450 \times \text{Rs. } 10 \times \frac{2}{100} = \text{Rs. } 90 \)
**Second Scenario: After Selling and Reinvesting**
Sundar sold his 450 shares when the market price rose to Rs. 23 per share.
Selling price of 450 shares \( = 450 \times \text{Rs. } 23 = \text{Rs. } 10,350 \)
He invested this amount (Rs. 10,350) in new shares: 25 shares paying 10% per annum, available at Rs. 18 each. This "25 shares" likely refers to the face value of the new shares.
Number of new shares bought \( = \frac{\text{Investment amount}}{\text{Market value per new share}} \)
Number of new shares bought \( = \frac{\text{Rs. } 10,350}{\text{Rs. } 18} = 575 \text{ shares} \)
Now, calculate the new income from these 575 shares, with a face value of Rs. 25 and a dividend rate of 10%.
New income \( = \) Number of new shares \( \times \) Face value of new share \( \times \) New dividend rate
New income \( = 575 \times \text{Rs. } 25 \times \frac{10}{100} \)
New income \( = \frac{575 \times 25 \times 10}{100} = \frac{575 \times 25}{10} = \frac{14375}{10} = \text{Rs. } 1,437.50 \)
**Change in Income**
Change in income \( = \) New income \( - \) Initial income
Change in income \( = \text{Rs. } 1,437.50 - \text{Rs. } 90 = \text{Rs. } 1,347.50 \)
This positive change shows that his new investment strategy was successful.
In simple words: First, figure out how much money Sundar made from his shares before he sold them. Then, calculate how much money he made after buying new shares with the sales money. The difference is the change in his income.

🎯 Exam Tip: Break down complex problems into clear, sequential steps (original income, sale proceeds, new investment, new income) to avoid errors, and pay close attention to whether the given share value is face value, market value, or total value.

Question 7. A man invests Rs. 13,500 partly in 6% of Rs. 100 shares at Rs. 140 and partly in 5% of Rs. 100 shares at Rs. 125. If his total income is Rs. 560, how much has he invested in each?
Answer: Let the amount invested in the 6% shares be \( x \) rupees. Then, the remaining amount, \( \text{Rs. } (13,500 - x) \), is invested in the 5% shares. We will calculate the income from each part and set their sum equal to the total income given.
**Part 1: 6% of Rs. 100 shares at Rs. 140**
Amount invested \( = x \)
Face value of a share \( = \text{Rs. } 100 \)
Market value of a share \( = \text{Rs. } 140 \)
Dividend rate \( = 6\% \)
Number of shares \( = \frac{\text{Amount invested}}{\text{Market value of a share}} = \frac{x}{140} \)
Income from 6% shares \( = \) Number of shares \( \times \) Face value \( \times \) Dividend rate
Income from 6% shares \( = \frac{x}{140} \times \text{Rs. } 100 \times \frac{6}{100} \)
Income from 6% shares \( = \frac{600x}{14000} = \frac{6x}{140} = \frac{3x}{70} \)
**Part 2: 5% of Rs. 100 shares at Rs. 125**
Amount invested \( = \text{Rs. } (13,500 - x) \)
Face value of a share \( = \text{Rs. } 100 \)
Market value of a share \( = \text{Rs. } 125 \)
Dividend rate \( = 5\% \)
Number of shares \( = \frac{\text{Amount invested}}{\text{Market value of a share}} = \frac{13,500 - x}{125} \)
Income from 5% shares \( = \) Number of shares \( \times \) Face value \( \times \) Dividend rate
Income from 5% shares \( = \frac{13,500 - x}{125} \times \text{Rs. } 100 \times \frac{5}{100} \)
Income from 5% shares \( = \frac{500(13,500 - x)}{12500} = \frac{5(13,500 - x)}{125} = \frac{13,500 - x}{25} \)
**Total Income**
Given that the total income is Rs. 560.
Total income \( = \) Income from 6% shares \( + \) Income from 5% shares
\( 560 = \frac{3x}{70} + \frac{13,500 - x}{25} \)
To solve for \( x \), find a common denominator for 70 and 25, which is 350.
Multiply the first term by \( \frac{5}{5} \) and the second term by \( \frac{14}{14} \):
\( 560 = \frac{3x \times 5}{70 \times 5} + \frac{(13,500 - x) \times 14}{25 \times 14} \)
\( 560 = \frac{15x}{350} + \frac{189,000 - 14x}{350} \)
\( 560 = \frac{15x + 189,000 - 14x}{350} \)
\( 560 = \frac{x + 189,000}{350} \)
Now, multiply both sides by 350:
\( x + 189,000 = 560 \times 350 \)
\( x + 189,000 = 196,000 \)
Subtract 189,000 from both sides:
\( x = 196,000 - 189,000 \)
\( x = 7,000 \)
So, the amount invested in 6% stock \( = \text{Rs. } 7,000 \)
And the amount invested in 5% stock \( = \text{Rs. } 13,500 - \text{Rs. } 7,000 = \text{Rs. } 6,500 \)
It's important to set up equations carefully when dealing with combined investments.
In simple words: We split the total money into two parts and named one part 'x'. Then we wrote down how much money would be earned from each part. We added these earnings and made it equal to the total income given, then solved to find out how much was invested in each part.

🎯 Exam Tip: For problems involving splitting an investment, using a variable (like \( x \)) for one part and the total minus \( x \) for the other part simplifies the setup of equations.

Question 8. Babu sold some 100 Shares at a 10% discount and invested his sales proceeds in 15% of Rs. 50 shares at Rs. 33. Had he sold his shares at a 10% premium instead of a 10% discount, he would have earned Rs. 450 more. Find the number of shares sold by him.
Answer: Let \( x \) be the number of shares Babu sold. The face value of each share is Rs. 100.
**Scenario 1: Selling at a 10% discount**
Selling price of one share \( = \text{Rs. } 100 - (10\% \text{ of Rs. } 100) = \text{Rs. } 100 - \text{Rs. } 10 = \text{Rs. } 90 \)
Total selling price of \( x \) shares \( = \text{Rs. } 90x \)
This amount is invested in new shares (face value Rs. 50, dividend rate 15%) available at Rs. 33 each.
Number of new shares bought \( = \frac{\text{Amount invested}}{\text{Market value per new share}} = \frac{90x}{33} \)
Income from these new shares (Income 1) \( = \) Number of new shares \( \times \) Face value \( \times \) Dividend rate
Income 1 \( = \frac{90x}{33} \times \text{Rs. } 50 \times \frac{15}{100} \)
Income 1 \( = \frac{90x \times 50 \times 15}{33 \times 100} = \frac{67500x}{3300} = \frac{675x}{33} = \frac{225x}{11} \)
**Scenario 2: Selling at a 10% premium**
Selling price of one share \( = \text{Rs. } 100 + (10\% \text{ of Rs. } 100) = \text{Rs. } 100 + \text{Rs. } 10 = \text{Rs. } 110 \)
Total selling price of \( x \) shares \( = \text{Rs. } 110x \)
This amount is invested in the same type of new shares (face value Rs. 50, dividend rate 15%) available at Rs. 33 each.
Number of new shares bought \( = \frac{\text{Amount invested}}{\text{Market value per new share}} = \frac{110x}{33} \)
Income from these new shares (Income 2) \( = \) Number of new shares \( \times \) Face value \( \times \) Dividend rate
Income 2 \( = \frac{110x}{33} \times \text{Rs. } 50 \times \frac{15}{100} \)
Income 2 \( = \frac{110x \times 50 \times 15}{33 \times 100} = \frac{82500x}{3300} = \frac{825x}{33} = 25x \)
**Comparing the incomes**
According to the problem, if he had sold at a premium, he would have earned Rs. 450 more.
Income 2 \( - \) Income 1 \( = \text{Rs. } 450 \)
\( 25x - \frac{225x}{11} = 450 \)
Find a common denominator, which is 11:
\( \frac{25x \times 11}{11} - \frac{225x}{11} = 450 \)
\( \frac{275x - 225x}{11} = 450 \)
\( \frac{50x}{11} = 450 \)
Now, solve for \( x \):
\( x = \frac{450 \times 11}{50} \)
\( x = 9 \times 11 \)
\( x = 99 \)
So, Babu sold 99 shares.
In simple words: We calculated Babu's yearly income for two different ways of selling his original shares (at a discount and at a premium). The problem told us the difference in these two incomes, which helped us set up an equation to find out how many shares he actually sold.

🎯 Exam Tip: Always clearly define your variable (e.g., \( x \) for the number of shares) and carefully set up separate income calculations for each scenario before forming an equation based on the given difference.

Question 9. Which is better investment? 7% of Rs. 100 shares at Rs. 120 (or) 8% of Rs. 100 shares at Rs. 135.
Answer: To compare two investments, we need to calculate the income generated by each for the same amount of money invested. Let's assume a convenient total investment amount that is a multiple of both Rs. 120 and Rs. 135 to make calculations easier. A simple way is to consider a common investment value like \( \text{Rs. } 120 \times 135 \), or simply calculate the income per Rs. 100 invested. The source uses \( \text{Rs. } 120 \times 135 \) as a common base investment. This approach ensures a fair comparison.
Let the total investment be \( \text{Rs. } 120 \times 135 \).
**Case (i): 7% of Rs. 100 shares at Rs. 120**
For every Rs. 120 invested, you get shares with a face value that yields 7% dividend. The income is 7% of the face value represented by the investment.
Income from 7% shares \( = \frac{\text{Dividend rate}}{\text{Market value}} \times \text{Face value} \times \text{Total Investment} \)
Income from 7% shares \( = \frac{7}{120} \times \text{Rs. } 100 \times (\frac{\text{Total Investment}}{\text{Face Value}}) \) - No, this is incorrect. The dividend rate is on face value. A simpler way: Income from Rs. 120 investment is \( \frac{\text{Rs. } 100 \times 7\%}{\text{Rs. } 120} \times \text{Total Investment} \). The source's calculation implies income per share and then multiplying by a derived number of shares. Let's follow the calculation shown:
Income for a total investment of \( \text{Rs. } 120 \times 135 \)
Income \( = \frac{\text{Rate of dividend}}{\text{Market Value of one share}} \times \text{Face Value of one share} \times \text{Total Investment} \)
Income from 7% shares \( = \frac{7}{120} \times \text{Rs. } 100 \times \text{Total Investment} \) - This implies the 7% is on the market value, which is usually not true for dividends. Dividends are on face value. Let's re-read: "7% of Rs. 100 shares at Rs. 120". This means face value is Rs. 100, dividend rate is 7%, market value is Rs. 120.
Let's use the standard method: calculate the income per share and then scale. The source's formula for income, \( \frac{7}{120} \times 120 \times 135 \), simplifies to \( 7 \times 135 \), which means it's effectively calculating (Face Value * Dividend Rate / Market Value) * Investment if we simplify. The 100 (face value) is missing in the source's simplified formula. Let's apply a general formula to ensure accuracy: Annual return percentage on investment = (Dividend per share / Market value per share) * 100.
**Using the given calculation in the source:**
Let the investment be \( \text{Rs. } 120 \times 135 \).
Income for Case (i) \( = 7 \times 135 = \text{Rs. } 945 \)
Income for Case (ii) \( = 8 \times 120 = \text{Rs. } 960 \)
This calculation implies the formula is: Rate of Dividend \( \times \text{ (Investment Amount / Market Value of one share)} \). However, the dividend rate is applied to the Face Value, not the Market Value directly. The problem statement itself seems to imply the "7% of Rs. 100 shares" means a 7% dividend on a Rs. 100 face value share. The calculation in the source is a simplified comparison, where the Rs. 100 face value (and number of shares logic) is implicit.
Let's use a consistent logic: **Income Rate (Yield) = (Dividend Rate * Face Value) / Market Value**.
**Case (i):** 7% of Rs. 100 shares at Rs. 120
Dividend per share \( = 7\% \text{ of Rs. } 100 = \text{Rs. } 7 \)
Yield 1 \( = \frac{\text{Rs. } 7}{\text{Rs. } 120} \times 100\% \approx 5.83\% \)
**Case (ii):** 8% of Rs. 100 shares at Rs. 135
Dividend per share \( = 8\% \text{ of Rs. } 100 = \text{Rs. } 8 \)
Yield 2 \( = \frac{\text{Rs. } 8}{\text{Rs. } 135} \times 100\% \approx 5.93\% \)
Since 5.93% \( > \) 5.83%, the second investment is better. The source's calculation gives: Income \( = \text{Rs. } 960 \) for Case (ii) vs \( \text{Rs. } 945 \) for Case (i). Both methods lead to the same conclusion: **8% of Rs. 100 shares at Rs. 135 is the better investment.** It generates more income for the same amount of investment.
In simple words: To find out which investment is better, we compare how much money you earn for every rupee you put in. We calculate the percentage return for each option and choose the one that gives a higher percentage.

🎯 Exam Tip: When comparing investments, always calculate the percentage yield (return on actual investment) for each option to make a fair comparison, as dividend rates alone can be misleading if market values differ.

Question 10. Which is better investment? 20% stock at 140 (or) 10% stock at 70.
Answer: To determine the better investment, we compare the income generated by each stock for a fixed amount of investment. Let's assume a total investment amount for comparison. A convenient amount would be \( \text{Rs. } 140 \times 70 \).
**Case (i): 20% stock at Rs. 140**
This means for every Rs. 140 invested, you get shares that yield 20% of their face value. Assuming face value is Rs. 100 (standard for stock unless specified otherwise), income per Rs. 140 investment is (20% of Rs. 100) = Rs. 20. So, the yield is \( \frac{\text{Rs. } 20}{\text{Rs. } 140} \).
Using the source's simplified calculation (similar to Q9):
Income from 20% stock at 140 \( = \frac{20}{140} \times 140 \times 70 = \text{Rs. } 1,400 \)
**Case (ii): 10% stock at Rs. 70**
Similarly, for every Rs. 70 invested, you get shares yielding 10% of their face value (assuming Rs. 100 face value). Income per Rs. 70 investment is (10% of Rs. 100) = Rs. 10. So, the yield is \( \frac{\text{Rs. } 10}{\text{Rs. } 70} \).
Income from 10% stock at 70 \( = \frac{10}{70} \times 140 \times 70 = \text{Rs. } 1,400 \)
In both cases, for the same investment of \( \text{Rs. } 140 \times 70 \), both stocks give the same income of Rs. 1,400. This means both investments are equally good, or equivalent shares.
In simple words: When we compare two investment options by putting the same amount of money into each, if they both give us the same profit, then they are equally good investments.

🎯 Exam Tip: For problems comparing stock investments, calculate the effective percentage return on the market price (yield) for each option. If the yields are the same, the investments are equivalent.