Every month, Sunaina invests `30%` of her monthly income in a gold, scheme, and pays `15%` as house rent. Out of the remaining monthly incomes, she spends on groceries and paying bills in the ratio of `5:6`. If the amount spent on groceries in a year is ₹96,000, then what is the amount that, she invests in gold scheme every month?

Options

A. ₹ 8,400
B. ₹ 7,200
C. ₹ 10,800
D. ₹ 9,600

Answer

To solve the problem step by step, we will follow the information provided and perform the necessary calculations.

### Step 1: Define Monthly Income
Let Sunaina's monthly income be represented as \( 100x \).

### Step 2: Calculate Investment in Gold Scheme
Sunaina invests \( 30\% \) of her monthly income in a gold scheme. Therefore, the amount she invests in the gold scheme each month is:
\[ \text{Investment in Gold Scheme} = 30\% \text{ of } 100x = 30x \]

### Step 3: Calculate House Rent
Sunaina pays \( 15\% \) of her monthly income as house rent. Thus, the amount she pays for house rent is:
\[ \text{House Rent} = 15\% \text{ of } 100x = 15x \]

### Step 4: Calculate Remaining Income
Now, we calculate the remaining income after her investments and house rent:
\[ \text{Remaining Income} = 100x - (30x + 15x) = 100x - 45x = 55x \]

### Step 5: Ratio of Spending on Groceries and Bills
The remaining income is spent on groceries and bills in the ratio of \( 5:6 \). The total parts in this ratio are:
\[ 5 + 6 = 11 \text{ parts} \]

### Step 6: Calculate Value of Each Part
Since the remaining income is \( 55x \), we can find the value of one part:
\[ \text{Value of 1 part} = \frac{55x}{11} = 5x \]

### Step 7: Calculate Amount Spent on Groceries
The amount spent on groceries (5 parts) is:
\[ \text{Amount Spent on Groceries} = 5 \text{ parts} = 5 \times 5x = 25x \]

### Step 8: Relate Groceries Spending to Yearly Amount
We know that the amount spent on groceries in a year is ₹96,000. Therefore, the monthly amount spent on groceries is:
\[ \text{Monthly Groceries Spending} = \frac{96000}{12} = 8000 \]

### Step 9: Set Up Equation for \( x \)
Now, we equate the amount spent on groceries to the monthly spending:
\[ 25x = 8000 \]

### Step 10: Solve for \( x \)
To find \( x \), we divide both sides by 25:
\[ x = \frac{8000}{25} = 320 \]

### Step 11: Calculate Investment in Gold Scheme
Finally, we can find the amount that Sunaina invests in the gold scheme each month:
\[ \text{Investment in Gold Scheme} = 30x = 30 \times 320 = 9600 \]

### Conclusion
Thus, the amount that Sunaina invests in the gold scheme every month is ₹9600.

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