Rimi and Simi spent `60%` and `75%` of their respective monthly salaries. Simi kept ` 60%` of the remaining as savings and gave the remaining ₹2100 to her sister What was Rimi’s monthly expenditure if her monthly salary was `25% `less than that of Simi?

Options

A. ₹ 9450
B. ₹18800
C. ₹ 20700
D. ₹21200

Answer

To solve the problem step by step, we will define the variables and calculate the required values based on the information given.

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

### Step 2: Calculate Rimi's Monthly Salary
Since Rimi's monthly salary is 25% less than Simi's, we can express Rimi's salary \( R \) as:
\[ R = S - 0.25S = 0.75S \]

### Step 3: Calculate Expenditures
Simi spends 75% of her salary. Therefore, Simi's expenditure \( E_S \) is:
\[ E_S = 0.75S \]
Rimi spends 60% of her salary. Therefore, Rimi's expenditure \( E_R \) is:
\[ E_R = 0.60R = 0.60 \times 0.75S = 0.45S \]

### Step 4: Calculate Remaining Salaries
After their expenditures, the remaining salaries for Simi and Rimi are:
- Simi's remaining salary:
\[ R_S = S - E_S = S - 0.75S = 0.25S \]
- Rimi's remaining salary:
\[ R_R = R - E_R = 0.75S - 0.45S = 0.30S \]

### Step 5: Calculate Simi's Savings and Amount Given to Her Sister
Simi saves 60% of her remaining salary:
\[ \text{Savings of Simi} = 0.60 \times 0.25S = 0.15S \]
The remaining amount after savings, which Simi gives to her sister, is:
\[ \text{Amount given to sister} = R_S - \text{Savings} = 0.25S - 0.15S = 0.10S \]
According to the problem, this amount is ₹2100:
\[ 0.10S = 2100 \]

### Step 6: Solve for Simi's Salary
To find Simi's salary \( S \):
\[ S = \frac{2100}{0.10} = 21000 \]

### Step 7: Calculate Rimi's Monthly Expenditure
Now that we have Simi's salary, we can find Rimi's salary:
\[ R = 0.75S = 0.75 \times 21000 = 15750 \]
Now we can find Rimi's monthly expenditure:
\[ E_R = 0.60R = 0.60 \times 15750 = 9450 \]

### Final Answer
Rimi’s monthly expenditure is ₹9450.

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