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.

Question

A bought a phone from a store and paid $\frac{1}{6}$ of the price using UPI, $\frac{1}{3}$ of the price in cash, and the remaining balance a year later. He also paid 10% interest on the remaining balance after one year. What was the original price of the phone?

Answer 1

Instead of tracking old and new income in separate stages, let's build a clean picture of the two conversions the person makes and read off the answer from the totals.

He starts with Rs. 10,000 in 4% debentures, which pays him a fixed Rs. 400 every year (that is simply $4\%$ of $10000$). On 1st Jan 1970 he splits this holding into two parts and swaps both parts into new instruments.

First conversion, 3/4 of the holding: Face value moved = $10000 \times \frac{3}{4} = 7500$. Sold at a 6% discount, so cash received = $7500 \times 0.94 = 7050$. This buys steel shares at Rs. 470 each: $7050 \div 470 = 15$ shares. Income from these shares = $15 \times 16 = 240$ per year.
Second conversion, remaining 1/4 of the holding: Face value moved = $10000 \times \frac{1}{4} = 2500$. Sold at Rs. 105 (a 5% premium over face value), so cash received = $2500 \times 1.05 = 2625$. This buys bonds at Rs. 75 each: $2625 \div 75 = 35$ bonds. Income from these bonds = $35 \times 5 = 175$ per year.

Now add up the two new income streams: $240 + 175 = 415$. This Rs. 415 replaces the old Rs. 400 he was earning from the debentures.

Comparing the two: $415 - 400 = 15$. Since the new figure is larger, his income has gone up, not down, by Rs. 15.

Let's summarize:

Old annual income from debentures: Rs. 400.
New annual income from 15 shares plus 35 bonds: Rs. 240 + Rs. 175 = Rs. 415.
Net change: an increase of Rs. 15.

So the correct answer is a Rs. 15 increase in his annual income, matching option (3).

\[ \boxed{\text{Rs. 15 increase}} \]

Answer 2

Instead of tracking old and new income in separate stages, let's build a clean picture of the two conversions the person makes and read off the answer from the totals.

He starts with Rs. 10,000 in 4% debentures, which pays him a fixed Rs. 400 every year (that is simply $4\%$ of $10000$). On 1st Jan 1970 he splits this holding into two parts and swaps both parts into new instruments.

First conversion, 3/4 of the holding: Face value moved = $10000 \times \frac{3}{4} = 7500$. Sold at a 6% discount, so cash received = $7500 \times 0.94 = 7050$. This buys steel shares at Rs. 470 each: $7050 \div 470 = 15$ shares. Income from these shares = $15 \times 16 = 240$ per year.
Second conversion, remaining 1/4 of the holding: Face value moved = $10000 \times \frac{1}{4} = 2500$. Sold at Rs. 105 (a 5% premium over face value), so cash received = $2500 \times 1.05 = 2625$. This buys bonds at Rs. 75 each: $2625 \div 75 = 35$ bonds. Income from these bonds = $35 \times 5 = 175$ per year.

Now add up the two new income streams: $240 + 175 = 415$. This Rs. 415 replaces the old Rs. 400 he was earning from the debentures.

Comparing the two: $415 - 400 = 15$. Since the new figure is larger, his income has gone up, not down, by Rs. 15.

Let's summarize:

Old annual income from debentures: Rs. 400.
New annual income from 15 shares plus 35 bonds: Rs. 240 + Rs. 175 = Rs. 415.
Net change: an increase of Rs. 15.

So the correct answer is a Rs. 15 increase in his annual income, matching option (3).

\[ \boxed{\text{Rs. 15 increase}} \]

Over Number	Run Rate
N-2	8.00
N	7.43
N+2	8.11
N+4	8.45
N+6	8.08

Show Hint

The Correct Option is C

Solution and Explanation

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