Loading Maths 1. A man buys Rs. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. What is the market value of each share? A. Rs.12 B. Rs.18 C. Rs.15 D. Rs.21

Here is the answer and explanation

Explanation :

Face value of each share = Rs.20

Dividend per share = 9% of 20 = $\dfrac{9\times 20}{100} = \dfrac{9}{5}$

He needs to have an interest of 12% on his money

$\text{ie, Money Paid for a share} \times \dfrac{12}{100}= \dfrac{9}{5}$

$\text{Money Paid for a share} = \dfrac{9}{5} \times \dfrac{100}{12} = 15$

ie, Market Value of the share = Rs.15

 2. A man invested Rs.1552 in a stock at 97 to obtain an income of Rs.128. What is the dividend from the stock? A. None of these B. 9.7% C. 7.5% D. 8%

Here is the answer and explanation

Explanation :

By investing Rs.1552, income = Rs.128

$\text{By investing Rs.97, income = }\dfrac{128\times 97}{1552} = 8$

ie, dividend = 8%

 3. The cost price of a Rs. 100 stock at 4 discount, when brokerage is $\dfrac{1}{5}\%$ is A. Rs. 96.25 B. Rs. 96.2 C. Rs. 97.25 D. Rs. 97.5

Here is the answer and explanation

Explanation :

$\text{Cost Price = }100 - 4 + \dfrac{1}{5} = 96.2$

 4. In order to obtain an income of Rs. 650 from 10% stock at Rs. 96, one must make an investment of A. Rs. 3100 B. Rs. 6500 C. Rs. 6240 D. Rs. 9600

Here is the answer and explanation

Explanation :

Market Value = Rs. 96.

Required Income = Rs. 650.

Here face value is not given. Take face value as Rs.100 if it is not given in the question

To obtain Rs.10 (ie,10% of the face value 100), investment = Rs.96

$\text{To obtain Rs.650, investment = }\dfrac{96}{10} \times 650 = 6240$

 5. By investing in $16\dfrac{2}{3}\%$ stock at 64, one earns Rs. 1500. The investment made is A. Rs. 9600 B. Rs. 7500 C. Rs. 5640 D. Rs. 5760

Here is the answer and explanation

Explanation :

Market Value = Rs.64

Face Value is not given and hence take it as Rs.100

$16\dfrac{2}{3}\% \text{ of the face value = }\dfrac{50}{3}$

$\text{ie, to earn }\dfrac{50}{3},\text{ investment = }Rs.64$

$\text{Hence, to earn Rs.1500, investment needed = }\dfrac{64 \times 3 \times 1500}{50} = 5760$

 6. A man invested Rs. 4940 in Rs. 10 shares quoted at Rs. 9.50. If the rate of dividend be 14%, his annual income is A. Rs.728 B. Rs.648 C. Rs.720 D. Rs.622

Here is the answer and explanation

Explanation :

Market Value of a share = Rs.9.50

Investment = Rs.4940

Number of shares = 4940/9.50 = 520

Face Value of a share = Rs.10

dividend = 14%

$\text{dividend per share = }\dfrac{(10 \times 14)}{100}\text{ = Rs. 1.4}$

His annual income = 520 × 1.4 = Rs.728

 7. A man invests some money partly in 12% stock at 105 and partly in 8% stock at 88. To obtain equal dividends from both, he must invest the money in the ratio: A. 31 : 44 B. 31 : 27 C. 16 : 15 D. 35 : 44

Here is the answer and explanation

Explanation :

----------------------------------------------
Solution 1
----------------------------------------------

In case of stock1, if he invest Rs.105, he will get a dividend of Rs.12 (assume face value = 100)

In case of stock2, if he invest Rs.88, he will get a dividend of Rs.8 (assume face value = 100)

ie, if he invest Rs.(88*12)/8, he will get a dividend of Rs.12

Required ratio = 105 : (88 × 12)/8 = 105 : (11 × 12) = 35 : (11 × 4) = 35 : 44

----------------------------------------------
Solution 2
----------------------------------------------
Let the amount of money he invest in 12% stock = P

Then, Number of shares = P/105 (where 105 is the market value per share)

Total dividend = (P/105) × 12 (Assume face value = Rs.100 and hence dividend per share = Rs.12)

Let the amount of money he invest in 8% stock = Q

Then, Number of shares = Q/88 (where 88 is the market value per share)

Total dividend = (Q/88)× 8 (Assume face value = Rs.100 and hence dividend per share = Rs.8)

If both needs to give equal dividends,

$\dfrac{P}{105} × 12 = \dfrac{Q}{88} × 8$

$\dfrac{P}{Q} = \dfrac{8 × 105}{88 × 12} = \dfrac{105}{11 × 12} = \dfrac{35}{11 × 4} = \dfrac{35}{44}$

P:Q = 35:44

 8. A man bought 40 shares of Rs. 60 at 5 discount, the rate of dividend being $12\dfrac{1}{2}\%$The rate of interest obtained is A. 13.64% B. 15.5% C. 14% D. 14.25%

Here is the answer and explanation

Explanation :

Face Value of a share = Rs.60

He bought each share at Rs.60 - Rs.5 = Rs.55

Number of shares = 40

$\text{Dividend = }12\dfrac{1}{2}\% = \dfrac{25}{2}\%$

$\text{Dividend per share = }\dfrac{60 \times 25}{2 \times 100} = Rs. 7.5$

Total dividend = (40 × 7.5)

ie, He got a dividend of (40 × 7.5) for an investment of Rs.(40 × 55)

$\text{Interest obtained = }\dfrac{40 \times 7.5 \times 100}{40 \times 55} = 13.64\%$

 9. By investing Rs. 1800 in 9% stock, Syam earns Rs. 120. The stock is then quoted at A. Rs.135 B. Rs. 96 C. Rs. 85 D. Rs. 122

Here is the answer and explanation

Explanation :

Assume that face value = Rs.100.

Dividend per share = Rs.9 (as it is a 9% stock)

By investing Rs. 1800, he earns Rs.120

$\text{Investment needed to earn Rs.9 = }\dfrac{1800 \times 9}{120}\text{ = Rs.135}$

ie, stock is then quoted (then market value) = Rs.135

 10. The market value of a 10.5% stock, in which an income of Rs. 756 is derived by investing Rs. 9000, brokerage being 1⁄4 %, is: A. Rs. 124.75 B. Rs. 108.25 C. Rs. 125.25 D. Rs. 112.20

Here is the answer and explanation

Explanation :

Assume that face value = Rs.100

Dividend per share = Rs.10.5 (as it is 10.5% stock)

By investing Rs.9000, earnings = Rs.756

$\text{To get an earning of Rs.10.5, investment required = }\dfrac{9000 \times 10.5}{756}\text{ = Rs.125}$

ie,market value of Rs. 100 stock = Rs.(125- 1/4) = Rs.124.75

 11. A 14% stock yielding 8% is quoted at: A. Rs. 125 B. Rs. 83.33 C. Rs. 120 D. Rs. 175

Here is the answer and explanation

Explanation :

Assume that face value = Rs.100 as it is not given

To earn Rs.8, money invested = Rs.100

$\text{To earn Rs.14, money invested = }\dfrac{100 \times 14}{8}\text{ = Rs.175}$

ie, market value of the stock = Rs.175

 12. Which is better investment: 11% stock at 143 or $9\dfrac{3}{4}\%$ stock at 120? A. $9\dfrac{3}{4}\%$ stock at 120 B. Cannot be compared, as the total amount of investment is not given. C. 11% stock at 143 D. Both are equally good

Here is the answer and explanation

Explanation :

Assume that face value of both stocks are Rs.100 as it is not given.

Hence, dividend per share in 1st case is Rs.11

and dividend per share in 2nd case is Rs.39/4

Assume that investment in each case is (Rs.143 × Rs.120)

$\text{Number of shares once can purchase in 1st case = }\dfrac{143 × 120}{143} = 120$

Income in 1st case = Rs.(120 × 11) = Rs.1320

$\text{Number of shares once can purchase in 2nd case = }\dfrac{143 × 120}{120} = 143$

Income in 2nd case = 143 × 39/4 = Rs.1394.25

$\text{Hence, }9\dfrac{3}{4}\%\text{ stock at 120 is better}$

 13. Sakshi invests a part of Rs. 12,000 in 12% stock at Rs. 120 and the remainder in 15% stock at Rs. 125. If his total dividend per annum is Rs. 1360, how much does he invest in 12% stock at Rs. 120? A. Rs. 6000 B. Rs. 4500 C. Rs. 5500 D. Rs. 4000

Here is the answer and explanation

Explanation :

Let Sakshi invests Rs.x in 12% stock

and he invests (12000-x) in 15% stock

Assume that face value of both stocks are Rs.100 as it is not given.

Hence, dividend per share in 1st case is Rs.12

and dividend per share in 2nd case is Rs.15

Number of 12% shares he can purchase with Rs.x = x/120

$\text{Total dividend from 12% shares = }\dfrac{x \times 12}{120}$

Number of 15% shares he can purchase with Rs.(12000-x) = (12000-x)/125

$\text{Total dividend from 15% shares = }\dfrac{(12000-x) \times 15}{125}$

Total dividend = Rs.1360

\begin{align}&\dfrac{x \times 12}{120} + \dfrac{(12000-x) \times 15}{125} = 1360\\\\ &\dfrac{x}{10} + \dfrac{(12000-x) \times 3}{25} = 1360\\\\ &5x + 6(12000-x) = 1360 \times 50\\\\ &5x + 72000-6x = 68000\\\\ &x = 4000\end{align}

 14. Rs. 9800 are invested partly in 9% stock at 75 and 10% stock at 80 to have equal amount of incomes. The investment in 9% stock is: A. Rs. 4800 B. Rs. 5400 C. Rs. 5000 D. Rs. 5600

Here is the answer and explanation

Explanation :

Assume that face value of both stocks are Rs.100 as it is not given.

Hence, dividend per share in 1st case is Rs.9

and dividend per share in 2nd case is Rs.10

Let investment in 9% stock = Rs.x

and investment in 10% stock = Rs.(9800-x)

Market value of a 9% stock= Rs.75

Number of 9% stocks he can purchase with Rs.x = x/75

$\text{Total dividend from 9% stocks = }\dfrac{x \times 9}{75}$

Market value of a 10% stock = Rs.80

Number of 10% stocks he can purchase with Rs.(9800-x) = (9800-x)/80

$\text{Total dividend from 10% stocks = }\dfrac{(9800-x) \times 10}{80}$

incomes fom both of the investments is same

\begin{align}&\dfrac{x \times 9}{75} = \dfrac{(9800-x) \times 10}{80}\\\\ &\dfrac{x \times 3}{25} = \dfrac{(9800-x)}{8}\\\\ &24x = 25 \times 9800 - 25x\\\\ &49x = 25 \times 9800\\\\ &x = \dfrac{25 \times 9800}{49} = 25 \times 200 = 5000\end{align}

ie, investment in 9% stock = Rs.5000

 15. A 6% stock yields 8%. The market value of the stock is: A. Rs. 133.33 B. Rs. 96 C. Rs. 75 D. Rs. 48

Here is the answer and explanation

Explanation :

Assume that face value = Rs.100 as it is not given

To earn Rs.8, money invested = Rs.100

$\text{To earn Rs.6, money invested = }\dfrac{100 × 6}{8} = \dfrac{100 × 3}{4} = 25 × 3 = 75$

ie, market value of the stock = Rs.75

 16. 12500 shares, of par value Rs. 20 each, are purchased from Ram by Mohan at a price of Rs. 25 each. Find the amount required to purchase the shares. A. 312500 B. 311500 C. 313500 D. 314500

Here is the answer and explanation

Explanation :

Face value of each share = Rs.20

Market value of each share = Rs.25

Number of shares = 12500

Amount required to purchase the shares = 12500 × 25 = 312500

 17. 12500 shares, of par value Rs. 20 each, are purchased from Ram by Mohan at a price of Rs. 25 each. If Mohan further sells the shares at a premium of Rs. 11 each, find his gain in the transaction. A. Rs. 75000 B. Rs. 70000 C. Rs. 85000 D. Rs. 65000

Here is the answer and explanation

Explanation :

Face value of each share = Rs.20

Market value of each share = Rs.25

Number of shares = 12500

Amount required to purchase the shares = 12500 × 25 = 312500

Mohan further sells the shares at a premium of Rs. 11 each

ie, Mohan further sells the shares at Rs.(20+11) = Rs.31 per share

total amount he gets by selling all the shares = 12500 × 31 = 387500

His gain = 387500 - 312500 = Rs.75000

 18. Find the annual dividend received by Nishita from 1200 preferred shares and 3000 common shares both of par value Rs. 50 each if the dividend paid on preferred shares is 10% and semi-annual dividend of 3½ % is declared on common shares. A. Rs. 18500 B. Rs. 16500 C. Rs. 14500 D. Rs. 19500

Here is the answer and explanation

Explanation :

Total number of preferred shares = 1200

Face value = Rs.50

dividend paid on preferred shares is 10%

$\text{Dividend per share = }\dfrac{50 \times 10}{100}\text{ = Rs.5}$

Total Dividend = 1200 × 5 = 6000

Total number of common shares = 3000

Face value = Rs.50

Semi-annual dividend of 3½ % is declared on common shares.

$\text{semi-annual dividend per share = }\dfrac{50 \times 7}{2 \times 100}\text{ = Rs.}\dfrac{7}{4}$

$\text{Total semi-annual dividend = }\dfrac{7}{4} \times 3000\text{ = Rs.5250}$

annual dividend = Rs.5250 × 2 = Rs.10500

Total dividend on all all shares(preferred and common) = 6000 + 10500 = Rs.16500

 19. A man invested Rs. 26000 in 5% stock at 104. He sold the stock when the price rose to Rs. 120 and invested the sale proceeds in 6% stock. By doing this his income increased by Rs. 2500. At what price did he purchase the second stock? A. Rs. 125 B. Rs. 48 C. Rs. 24 D. None of these

Here is the answer and explanation

Explanation :

Assuming that face value of the first stock = Rs.100 as it is not given in the question

Since it is a 5% stock, we can take the dividend per stock = Rs.5

Market Value of the first stock = Rs.104

Investment on the first stock = Rs.26000

Number of stocks purchases = 26000/104 = 250

His total income from all these stocks = Rs.250 × 5 = Rs.1250

He sells each of this stock at Rs.120

ie, amount he earns = Rs.120 × 250 = Rs.30000

He invest this Rs.30000 in 6% stock (here also face value is not given and hence take it as Rs.100)

His new income = Rs.(1250 + 2500) = Rs.3750

ie, By Rs.30000 of investment , he earns an income of Rs.3750

$\text{To get an income of Rs.6, investment needed = }\dfrac{30000 \times 6}{3750} = Rs.48$

This is the market value of the second stock

 20. Anu invested Rs. 32400 in 8% stock at 90. She sold out Rs. 18000 stock when the price rose to Rs 95 and the remaining stock at Rs.98. She invested the total sale proceeds in 10% stock at 96½. Find the change in income of Anu. A. Rs.2220 B. Rs.120 C. Rs.2720 D. Rs.720

Here is the answer and explanation

Explanation :

Since the face value of the stock is not given, we can take it as Rs.100

it is an 8% stock. ie, dividend per stock = Rs.8

Total investment = Rs.32400

Market Value = Rs.90

$\text{Amount of stock she purchased = }\dfrac{32400 × 100}{90}\text{ = Rs.36000}$

Number of shares she purchased = 32400/90 = 360

Total income = 360 × 8 = Rs.2880

She sold out Rs. 18000 stock when the price was Rs.95

$\text{Amount received by selling Rs.18000 stock at Rs.95 = }\dfrac{18000 × 95}{100}\text{ = Rs.17100}$

$\text{Amount received by selling remaining Rs.18000 stock at Rs.98 = }\dfrac{18000 × 98}{100}\text{ = Rs.17640}$

Total amount received = Rs. (17100 + 17640) = Rs. 34740

This Rs.34740 is invested in 10% stock at 96½

$\text{Number of shares = }\dfrac{34740}{\left(\dfrac{193}{2}\right)} = 360$

Total income from these stocks = 360 × 10 = Rs.3600

Change in income = Rs.3600 - Rs.2880 = Rs.720

 21. A man bought 20 shares of Rs. 50 at 5 discount, the rate of dividend being $13\dfrac{1}{2}\%$The rate of interest obtained is A. 12.5% B. 15% C. 15.5% D. 17%

Here is the answer and explanation

Explanation :

Face Value of a share = Rs.50

He bought each share at Rs.50 - Rs.5 = Rs.45

Number of shares = 20

$\text{Dividend = }13\dfrac{1}{2}\% = \dfrac{27}{2}\%$

$\text{Dividend per share = }\dfrac{50 \times 27}{2 \times 100} = Rs. 6.75$

Total dividend = (20 × 6.75)

ie, He got a dividend of (20 × 6.75) for an investment of Rs.(20 × 45)

$\text{Interest obtained = }\dfrac{20 \times 6.75 \times 100}{20 \times 45} = 15\%$

 22. Find the income on 7½ % stock of Rs. 2000 purchased at Rs. 80. A. Rs.6 B. Rs.160 C. Rs.148 D. Rs.150

Here is the answer and explanation

Explanation :

Face Value of the stock = Rs.2000

$\text{Dividend is 7}\dfrac{1}{2}\% = \dfrac{15}{2}\%\text{ of the face value}$

$\text{Dividend = }\dfrac{2000 \times 15 }{2 \times 100}\text{ = Rs.150}$

 23. John buys 100 shares of par value Rs. 5 each, of a company, which pays an annual dividend of 12% at such a price that he gets 10% on his investment. Find the market value of a share. A. Rs.6 B. Rs.12 C. Rs.4 D. Rs.8

Here is the answer and explanation

Explanation :

Face value of each share = Rs.5

$\text{Total dividend received by John = }100 \times 5 \times \dfrac{12}{100}\text{ = Rs.60}$

Let market value of 100 shares = Rs.x

$x \times \dfrac{10}{100} = 60$

x = 600

ie, Market value of 100 shares = Rs.600

Hence, Market value of each share = Rs.6

 24. A man invested Rs. 5050 in 5% stock at 99 and sold it when the price rose to Rs. 101. He invested the sale proceeds in 8% stock at 88. Find the change in man's income if the Brokerage is Rs. 2. A. 0 B. Rs.160 C. Rs.180 D. Rs.190

Here is the answer and explanation

Explanation :

Purchase price of the first stock = Rs.99 + Rs.2 = Rs.101

Number of stocks purchased in this case = 5050/101 = 50

Since the face value is not given, it can be taken as Rs.100. So, dividend per share = Rs.5

Income = 50 × 5 = Rs.250

Sale Price of the stock = 101-2 = 99

Amount received by selling the stock = 50 × 99 = 4950

Then he invests this Rs.4950 in 8% stock at 88

Purchase price of this stock = 88+2 = 90

Number of stocks purchased in this case = 4950/90 = 55

Since the face value is not given, it can be taken as Rs.100. So, dividend per share = Rs.8

Income = 55 × 8 = Rs.440

Change in income = 440-250 = Rs.190

 25. To produce an annual income of Rs. 800 from a 8% stock at 90, the amount of stock needed is: A. Rs.10000 B. Rs.14400 C. Rs.10800 D. Rs.16000

Here is the answer and explanation

Explanation :

Since face value is not given, take it as Rs.100.

As it is an 8% stock, income (dividend) per stock = Rs.8

ie, For an income of Rs.8,amount of stock needed = Rs.100

$\text{For an income of Rs.800, amount of stock needed = }\dfrac{100 \times 800}{8} = 10000$

 26. A man sells 4000 common shares of a Company x (each of par value Rs. 10), which pays a dividend of 40% at Rs. 30 per share. He invests the sale proceeds in ordinary shares of Company Y (each of par value Rs. 25) that pays a dividend of 15%. If the market value of Company Y is Rs. 15, find the number of shares of Company Y purchased by the man A. 8000 B. 12000 C. 16000 D. None of these

Here is the answer and explanation

Explanation :

Just too much information is given in the question to confuse. This is a straight and simple question

Market Value of Company X (his selling price) = Rs.30

Total shares sold = 4000

Amount he gets = Rs.(4000 × 30)

He invests this amount in ordinary shares of Company Y

Market Value of Company Y(His purchasing price) = 15

$\text{Number of shares of company Y which he purchases = }\dfrac{4000 × 30}{15} = 8000$

 27. A company issued 20000 shares of par value Rs. 10 each. If the total divided declared by the company is Rs.24000, find the rate of dividend paid by the company. A. 12% B. 12.5% C. 14% D. 14.5%

Here is the answer and explanation

Explanation :

Number of shares = 20000

Face value of each share = Rs.10

$\text{divided per share = }10 \times \dfrac{R}{100}\text{ where R is the rate of interest}$

$\text{Total divided = }20000 \times 10 \times \dfrac{R}{100}$

$20000 \times 10 \times \dfrac{R}{100} = 24000$

$\Rightarrow R = \dfrac{24000}{2000} = 12$

ie, divided = 12%

 28. A company declared a semi-annual dividend of 12%. Find the annual dividend of Sam owing 2000 shares of the company having a par value of Rs. 10 each. A. Rs.4800 B. Rs.2400 C. Rs.3600 D. None of these

Here is the answer and explanation

Explanation :

$\text{semi-annual dividend = }\dfrac{10 \times 12}{100}\text{ = Rs.1.2}$

Total semi-annual dividend = 2000 × 1.2 = Rs.2400

Total annual dividend = 2 × Rs.2400 = Rs.4800

 29. A company has issued 500 preferred shares and 400 common shares both of par value Rs. 100 each. The dividend on a preferred share and a common share is 8% and 12%, respectively. The company had a total profit of 150000 rupees out of which some amount was kept in reverse fund and the remaining disturbed as dividend. Find the amount kept in reserve fund. A. Rs.141200 B. Rs.160000 C. Rs.7200 D. Rs.182200

Here is the answer and explanation

Explanation :

Face value of each preferred share = 100

$\text{Dividend per preferred share = }\dfrac{100 \times 8}{100}$

$\text{Total dividend in all preferred shares = }\dfrac{500 \times 100 \times 8}{100} = Rs.4000$

Face value of each common share = 100

$\text{Dividend per common share = }\dfrac{100 \times 12}{100}$

$\text{Total dividend in all common shares = }\dfrac{400 \times 100 \times 12}{100}\text{ = Rs.4800}$

Total dividend = Rs.4000 + Rs.4800 = Rs.8800

amount kept in reserve fund = Rs.150000 - Rs.8800 = Rs.141200

 30. Arun invested Rs. 333000 in 5½ % stocks at 110 .If brokerage is Rs.1, what is his annual income from his investment. A. Rs.16500 B. Rs.12500 C. Rs.16000 D. Rs.18000

Here is the answer and explanation

Explanation :

Investment = Rs.333000

Since face value is not given, we can take it as Rs.100

and dividend per share = Rs.11/2

Market Value = 110 + 1 = 111

Number of shares purchased = 333000/111 = 3000

$\text{Total income = }3000 \times \dfrac{11}{2}\text{ = Rs.16500}$

 31. Find the income on 8% stock of Rs.1200 purchased at Rs.120? A. Rs.96 B. Rs.66 C. Rs.90 D. Rs.88

Here is the answer and explanation

Explanation :

Face Value = Rs.1200

Market Value = Rs.120

$\text{Dividend (income)= }\dfrac{1200 \times 8}{100}\text{ = Rs.96}$

victor otieno
2014-11-13 15:56:40
find the cost of RS 8750,8.5% stock at 92 (0) (0) Reply
srhri mhnndia
2014-10-08 06:21:16
Answering and discussing  make the thing clear. (0) (0) Reply
aakash
2014-01-23 21:06:54
Which is a better investment 14% stock at 95 or 15% stock at 105 (0) (0) Reply
Jay
2014-01-25 13:04:02
This is same as Q.12

Dividend per share in 1st case is Rs.14
Dividend per share in 2nd case is Rs.15

Number of shares one can purchase with Rs.(95*105)  in 1st case = (95*105) /95= 105
Number of shares one can purchase with Rs.(95*105)  in 2nd case = (95*105) /105 = 95

Income in 1st case = Rs.(14 × 105) = Rs.1470
Income in 2nd case = Rs.(15 × 95) = Rs.1425

So, 14% stock at 95 is better (0) (0) Reply

Add a new comment...  (Use Discussion Board for posting new aptitude questions.)

Name:
Email: (optional)

X View & Edit Profile Sign out
X 