Question

On 1st January 1969, a person purchases Rs. 10,000, 4% debentures. On 1st Jan. 1970, he sells 3/4 of it at a discount of 6% and invests the proceeds in steel shares at Rs. 470 per share. He sells the remaining debentures at Rs. 105 and purchases bonds at a price of Rs. 75 per bond. Each bond pays Rs. 5. Each share pays Rs. 16. Find the alteration in his annual income in 1970.

• A. Rs. 15 decrease
• B. Rs. 25 increase
• C. Rs. 15 increase
• D. None

Hint:

Work out the cash he gets from each debenture sale, convert that cash into whole shares or bonds bought, add up the two new incomes, and compare the total to the old Rs. 400.

Answer 1

The Correct Option is C

Step 1: Find the original annual income.
The person holds Rs. 10,000 face value of 4% debentures.
Annual income from these debentures is 4% of Rs. 10,000:
\[ 10000 \times \frac{4}{100} = 400 \]
So his original annual income is Rs. 400.

Step 2: Work out the sale of 3/4 of the debentures.
3/4 of Rs. 10,000 face value is:
\[ 10000 \times \frac{3}{4} = 7500 \]
This Rs. 7,500 face value is sold at a discount of 6%, meaning he gets only 94% of face value for it:
\[ 7500 \times \frac{94}{100} = 7050 \]
So he receives Rs. 7,050 from this sale.

Step 3: Invest this money in steel shares.
Steel shares cost Rs. 470 each. Number of shares he can buy:
\[ \frac{7050}{470} = 15 \]
He buys 15 shares. Each share pays Rs. 16 a year, so his income from shares is:
\[ 15 \times 16 = 240 \]

Step 4: Work out the sale of the remaining 1/4 of the debentures.
The remaining face value is:
\[ 10000 \times \frac{1}{4} = 2500 \]
This is sold at Rs. 105 (per 100 face value), meaning he gets 105% of face value:
\[ 2500 \times \frac{105}{100} = 2625 \]
So he receives Rs. 2,625 from this sale.

Step 5: Buy bonds with this money.
Bonds cost Rs. 75 each. Number of bonds he can buy:
\[ \frac{2625}{75} = 35 \]
He buys 35 bonds. Each bond pays Rs. 5 a year, so his income from bonds is:
\[ 35 \times 5 = 175 \]

Step 6: Find the new total annual income and compare.
New annual income = income from shares + income from bonds:
\[ 240 + 175 = 415 \]
Change in income = new income minus old income:
\[ 415 - 400 = 15 \]
Since 415 is greater than 400, his annual income increases by Rs. 15.

Step 7: Why the other options fail.
Option (1), a decrease of Rs. 15, is the reverse of what actually happens, his income goes up, not down.
Option (2), an increase of Rs. 25, comes from a wrong split or a wrong price used in one of the two purchases.
Option (4), None, is wrong since Rs. 15 increase is exactly what we get.

Final Answer:
His annual income increases by Rs. 15 in 1970. \[ \boxed{\text{Rs. 15 increase}} \]