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QUESTION: 1

A 14% stock yielding 8% is quoted at:

Solution:

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

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

To earn Rs.14, money invested =

100 ×14 / 8= Rs.175

ie, market value of the stock = Rs.175

QUESTION: 2

Which is better investment: 11% stock at 143 or 9(3/4%) stock at 120?

Solution:

Let investment in each case be Rs. (143 x 117).

Income in 1st case = Rs.11/143 x 143 x 117 = Rs. 1287.

Income in 2nd case = Rs.39/(4×117) x 143 x 117= Rs. 1394.25

Clearly, 9 3/4% stock at 117 is better.

QUESTION: 3

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?

Solution:

Let investment in 12% stock be Rs.x

Then, investment in 15% stock=Rs.(12000−x)

∴ 12/120 × x + 15/125 *(12000−x) = 1360

⇒ x/10 + 3/25(12000−x) = 1360

⇒ 5x + 72000 − 6x = 1360 × 50

⇒ x = 4000

QUESTION: 4

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:

Solution:

Let the investment in 9% stock be Rs.x Then,investment in 10% stock = Rs.(9800−x)

9/75 × x = 10/80 × (9800−x)

⇒ 3x/25 = (9800−x)/8

⇒24x = 9800 × 25 − 25x

⇒ 49x = 9800×25

⇒x = 5000

QUESTION: 5

A 6% stock yields 8%. The market value of the stock is:

Solution:

For an income of Rs. 8, investment = Rs. 100.

For an income of Rs. 6,

investment = Rs.(100/8 × 6)

= Rs.75

QUESTION: 6

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.

Solution:

Market value of a share = Rs. 25

Market value of 12500 shares = Rs. (25 x 12500) = Rs. 312500

Thus, the amount required to purchase 12500 shares = Rs. 312500

QUESTION: 7

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.

Solution:

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

QUESTION: 8

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.

Solution:

Total number of preferred shares = 1200

Face value = Rs.50

dividend paid on preferred shares is 10%

Dividend per share = 50 × 10/100 = 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.

semi-annual dividend per share =

50 × 7/2 × 100 = Rs.7/4

Total semi-annual dividend = 7/4 × 3000 = Rs.5250

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

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

= Rs.16500

QUESTION: 9

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?

Solution:

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

To get an income of Rs.6, investment needed = (30000 × 6)/3750 = Rs.48

QUESTION: 10

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.

Solution:

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

Amount of stock she purchased = (32400×100)/90 = 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

Amount received by selling Rs.18000 stock at Rs.95 = (18000×95)/100 = Rs.17100

Amount received by selling remaining Rs.18000 stock at Rs.98 = (18000×98)/100 = Rs.17640

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

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

Number of shares = 34740*(193/2) = 360

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

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

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