Sonal spent rs. 45760 on the interior decoration for her home, rs. 27896 on buying air conditioner and the remaining 28% of the total amount she had as cash with her. What was the total amount?

Options

A. a. rs. 98540
B. b. rs. 102300
C. c. rs. 134560
D. d. cannot be determined

Answer

To find the total amount Sonal had, we can follow these steps:

### Step 1: Understand the problem
Sonal spent Rs. 45,760 on interior decoration and Rs. 27,896 on an air conditioner. The remaining amount she had is 28% of her total cash. We need to find out what the total amount was.

### Step 2: Calculate total expenses
First, we need to calculate the total amount Sonal spent on both the interior decoration and the air conditioner.

\[ \text{Total Expenses} = \text{Interior Decoration} + \text{Air Conditioner} \]
\[ \text{Total Expenses} = 45760 + 27896 \]
\[ \text{Total Expenses} = 73656 \]

### Step 3: Determine the percentage spent
Since Sonal kept 28% of her total amount as cash, the percentage of the total amount that she spent is:

\[ \text{Percentage Spent} = 100\% - 28\% = 72\% \]

### Step 4: Set up the equation
Now we know that 72% of the total amount (let's call it \( x \)) is equal to her total expenses:

\[ 0.72x = 73656 \]

### Step 5: Solve for the total amount
To find \( x \), we can rearrange the equation:

\[ x = \frac{73656}{0.72} \]

Calculating this gives:

\[ x = 102300 \]

### Conclusion
Thus, the total amount Sonal had is Rs. 1,02,300.

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