Mr Scindia after selling 5.5% stock at Rs. 92 realizes Rs. 32200. Then he invested `(1)/(3)` of the amount in 4.5% stock at Rs. `92, (2)/(5)` of the amount at Rs. 115 in 5% stock and the remaining in 6% stock at Rs. 56. The change in his income is :

Options

A. Rs. 56 loss
B. Rs. 78 profit
C. Rs. 80 profit
D. Rs. 70 loss

Answer

To solve the problem step by step, we will follow the instructions given in the question regarding Mr. Scindia's investments and calculate the change in his income.

### Step 1: Calculate the total amount realized from selling the stock.
Mr. Scindia sells a 5.5% stock at Rs. 92 and realizes Rs. 32,200.

**Total amount realized = Rs. 32,200**

### Step 2: Determine the amount invested in each stock.
Mr. Scindia invests:
- \( \frac{1}{3} \) of the total amount in 4.5% stock
- \( \frac{2}{5} \) of the total amount in 5% stock
- The remaining amount in 6% stock

**Calculating each investment:**
1. **Investment in 4.5% stock:**
\[ \text{Amount invested} = \frac{1}{3} \times 32,200 = \frac{32,200}{3} = 10,733.33 \]

2. **Investment in 5% stock:**
\[ \text{Amount invested} = \frac{2}{5} \times 32,200 = \frac{64,400}{5} = 12,880 \]

3. **Remaining amount for 6% stock:**
\[ \text{Remaining amount} = 32,200 - (10,733.33 + 12,880) = 32,200 - 23,613.33 = 8,586.67 \]

### Step 3: Calculate the income from each stock.
1. **Income from 4.5% stock:**
\[ \text{Income} = \frac{10,733.33 \times 4.5}{100} = 483.00 \]

2. **Income from 5% stock:**
\[ \text{Income} = \frac{12,880 \times 5}{100} = 644.00 \]

3. **Income from 6% stock:**
\[ \text{Income} = \frac{8,586.67 \times 6}{100} = 515.20 \]

### Step 4: Calculate the total income after investments.
**Total income = Income from 4.5% stock + Income from 5% stock + Income from 6% stock**
\[ \text{Total income} = 483.00 + 644.00 + 515.20 = 1,642.20 \]

### Step 5: Calculate the original income from the 5.5% stock.
To find the original income from the 5.5% stock, we need to know how much he would earn from the original investment.

Let’s assume he had invested the entire Rs. 32,200 in 5.5% stock:
\[ \text{Original income} = \frac{32,200 \times 5.5}{100} = 1,771.00 \]

### Step 6: Calculate the change in income.
**Change in income = Total income after investments - Original income**
\[ \text{Change in income} = 1,642.20 - 1,771.00 = -128.80 \]

Thus, the change in Mr. Scindia's income is a decrease of Rs. 128.80.

### Final Answer:
The change in Mr. Scindia's income is Rs. -128.80.

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