Seema bought a mobile and got a discount of 18.5%. Had there been a 24% discount, she could have saved an additional ? 1650. How much did he pay for mobile?

Options

A. Rs. 22,800
B. Rs. 30000
C. Rs. 25,000
D. Rs. 24450

Answer

To solve the problem step by step, we will first define the variables and then use the information provided to find out how much Seema paid for the mobile.

### Step 1: Define Variables
Let the list price of the mobile be \( P \).

### Step 2: Calculate the Amount Paid with 18.5% Discount
The discount Seema received is 18.5%. Therefore, the amount she paid can be calculated as:
\[ \text{Amount Paid} = P - (18.5\% \text{ of } P) = P - 0.185P = 0.815P \]

### Step 3: Calculate the Amount Saved with 24% Discount
If there had been a 24% discount, the amount she would have paid is:
\[ \text{Amount Paid with 24% Discount} = P - (24\% \text{ of } P) = P - 0.24P = 0.76P \]

### Step 4: Calculate the Additional Savings
According to the problem, the additional savings with a 24% discount compared to the 18.5% discount is Rs. 1650. Therefore, we can set up the equation:
\[ \text{Amount Paid with 18.5% Discount} - \text{Amount Paid with 24% Discount} = 1650 \]
Substituting the expressions from Steps 2 and 3:
\[ 0.815P - 0.76P = 1650 \]

### Step 5: Simplify the Equation
Now, simplify the left side:
\[ 0.055P = 1650 \]

### Step 6: Solve for \( P \)
To find \( P \), divide both sides by 0.055:
\[ P = \frac{1650}{0.055} = 30000 \]

### Step 7: Calculate the Amount Paid by Seema
Now that we have the list price \( P \), we can find out how much Seema paid:
\[ \text{Amount Paid} = 0.815P = 0.815 \times 30000 = 24450 \]

### Final Answer
Seema paid Rs. 24450 for the mobile.

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