Mr. Shah's monthly income is Rs 54,550. In an entire year, he spends `32%` of his annual salary on groceries, `12%` on equipment repairs, `10%` on servant, and the half of remaining amount is invested in fixed in fixed deposit, what is the amount invested by him in fixed deposit?

Options

A. A)`Rs 1,50,558`
B. B)`Rs 1, 55, 240`
C. C)`Rs1,52,610`
D. D)`Rs 1,58,789`

Answer

To solve the problem step by step, we will follow the outlined process:

### Step 1: Calculate Mr. Shah's Annual Income
Mr. Shah's monthly income is given as Rs. 54,550. To find his annual income, we multiply his monthly income by 12 (the number of months in a year).

\[ \text{Annual Income} = \text{Monthly Income} \times 12 = 54,550 \times 12 = 654,600 \]

### Step 2: Calculate the Total Expenditure on Groceries, Equipment Repairs, and Servant
Mr. Shah spends a percentage of his annual income on groceries, equipment repairs, and servant. The percentages are as follows:
- Groceries: 32%
- Equipment Repairs: 12%
- Servant: 10%

First, we add these percentages together:

\[ \text{Total Expenditure Percentage} = 32\% + 12\% + 10\% = 54\% \]

### Step 3: Calculate the Remaining Income After Expenditures
To find the remaining income after these expenditures, we subtract the total expenditure percentage from 100%.

\[ \text{Remaining Percentage} = 100\% - 54\% = 46\% \]

### Step 4: Calculate the Amount of Remaining Income
Now, we calculate the amount corresponding to the remaining 46% of the annual income:

\[ \text{Remaining Income} = 46\% \text{ of } 654,600 = \frac{46}{100} \times 654,600 = 301,116 \]

### Step 5: Calculate the Amount Invested in Fixed Deposit
Mr. Shah invests half of the remaining income in a fixed deposit. Therefore, we need to calculate half of the remaining income:

\[ \text{Amount Invested in FD} = \frac{1}{2} \times 301,116 = 150,558 \]

### Final Answer
The amount invested by Mr. Shah in fixed deposit is Rs. 150,558.

---