A man bought a house in 5 lakh and gave it on rent. He save `12(1)/(2)%` of rent per month for maintenance and spend `Rs1660` on security per annum then find the monthly rent of person if he wants to earn `10%` of profit per annum on his total investment ?

Options

A. Rs. `4920`
B. Rs. `4590`
C. Rs. `4620`
D. Rs. `4500`

Answer

To solve the problem step by step, we will break down the information given and calculate the monthly rent required for the man to earn a profit.

### Step 1: Understand the Investment and Profit Requirement
The man bought a house for ₹5,00,000 and wants to earn a profit of 10% per annum on this investment.

**Calculation:**
- Total Investment = ₹5,00,000
- Desired Profit = 10% of ₹5,00,000 = (10/100) * 5,00,000 = ₹50,000 per annum

### Step 2: Calculate Monthly Profit Requirement
Since the profit is calculated annually, we need to convert this into a monthly profit.

**Calculation:**
- Monthly Profit = ₹50,000 / 12 = ₹4,166.67 (approximately)

### Step 3: Understand Maintenance and Security Costs
The man saves 12.5% of the rent for maintenance and spends ₹1,660 on security per annum.

**Calculation:**
- Maintenance Percentage = 12.5% = 12.5/100 = 1/8 of the rent (R)
- Annual Security Cost = ₹1,660
- Monthly Security Cost = ₹1,660 / 12 = ₹138.33 (approximately)

### Step 4: Set Up the Equation for Rent
The total expenses (maintenance + security) should be deducted from the rent to ensure the profit is achieved.

**Equation:**
Let R be the monthly rent.
- Maintenance = (1/8)R
- Monthly Security = ₹138.33
- Total Expenses = Maintenance + Monthly Security = (1/8)R + ₹138.33

The equation for profit can be set up as:
\[ R - \left( \frac{1}{8}R + 138.33 \right) = 4,166.67 \]

### Step 5: Simplify the Equation
Now, we will simplify the equation to find R.

**Calculation:**
\[ R - \frac{1}{8}R - 138.33 = 4,166.67 \]
\[ \frac{7}{8}R - 138.33 = 4,166.67 \]
\[ \frac{7}{8}R = 4,166.67 + 138.33 \]
\[ \frac{7}{8}R = 4,305 \]

### Step 6: Solve for R
To find the monthly rent R, we will multiply both sides by 8/7.

**Calculation:**
\[ R = 4,305 * \frac{8}{7} \]
\[ R = 4,305 * 1.142857 \]
\[ R = 4,920 \]

### Conclusion
The monthly rent that the man should charge is **₹4,920**.

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