Each month, Sania out of her monthly salary pays 25% towards rent and 40% of the remaining salary to her mother. She spends 40% of the remaining amount and saves the remaining in her bank account, if after the end of 5 months she saved in her bank account is. rs 1,08,000, how much did she pay towards the rent, per month?

Options

A. ₹30,000
B. ₹24,000
C. ₹16,000
D. ₹20,000

Answer

To solve the problem step by step, let's break down the calculations based on the information provided.

### Step 1: Define the Monthly Salary
Let Sania's monthly salary be represented as \( S \).

### Step 2: Calculate Rent Payment
Sania pays 25% of her monthly salary towards rent:
\[ \text{Rent} = 25\% \text{ of } S = \frac{25}{100} \times S = 0.25S \]

### Step 3: Calculate Remaining Salary After Rent
After paying rent, the remaining salary is:
\[ \text{Remaining Salary} = S - \text{Rent} = S - 0.25S = 0.75S \]

### Step 4: Calculate Payment to Mother
Sania gives 40% of the remaining salary to her mother:
\[ \text{Payment to Mother} = 40\% \text{ of } 0.75S = \frac{40}{100} \times 0.75S = 0.30S \]

### Step 5: Calculate Remaining Salary After Payment to Mother
The remaining salary after paying her mother is:
\[ \text{Remaining Salary} = 0.75S - 0.30S = 0.45S \]

### Step 6: Calculate Spending
Sania spends 40% of the remaining amount:
\[ \text{Spending} = 40\% \text{ of } 0.45S = \frac{40}{100} \times 0.45S = 0.18S \]

### Step 7: Calculate Savings
The amount saved after spending is:
\[ \text{Savings} = 0.45S - 0.18S = 0.27S \]

### Step 8: Calculate Total Savings After 5 Months
Over 5 months, the total savings would be:
\[ \text{Total Savings} = 5 \times \text{Savings per month} = 5 \times 0.27S = 1.35S \]

### Step 9: Set Up the Equation
According to the problem, after 5 months, Sania saved Rs. 1,08,000:
\[ 1.35S = 1,08,000 \]

### Step 10: Solve for Monthly Salary \( S \)
To find \( S \):
\[ S = \frac{1,08,000}{1.35} = 80,000 \]

### Step 11: Calculate Monthly Rent Payment
Now, we can calculate how much she pays towards rent each month:
\[ \text{Rent} = 0.25S = 0.25 \times 80,000 = 20,000 \]

### Final Answer
Sania pays Rs. 20,000 towards rent each month.

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