Successive discounts of `12(1)/(2)%` and `7(1)/(2)%` are given on the marked price of a cupboard. If the customer pays Rs. 2590, then what is the marked price ?

Options

A. Rs. 3108
B. Rs. 3148
C. Rs. 3200
D. Rs. 3600

Answer

To find the marked price of the cupboard after applying successive discounts of 12.5% and 7.5%, we can follow these steps:

### Step 1: Understand the Discounts
The marked price (MP) is initially set at 100%. The first discount is 12.5%, which means the customer pays 100% - 12.5% = 87.5% of the marked price after the first discount.

### Step 2: Calculate the Price After the First Discount
Let the marked price be MP. After the first discount of 12.5%, the price becomes:
\[ \text{Price after first discount} = MP \times \left( \frac{87.5}{100} \right) \]

### Step 3: Apply the Second Discount
The second discount is 7.5%. After applying this discount to the already reduced price, the customer pays:
\[ \text{Price after second discount} = \text{Price after first discount} \times \left( \frac{92.5}{100} \right) \]
Substituting the first discount calculation:
\[ \text{Price after second discount} = MP \times \left( \frac{87.5}{100} \right) \times \left( \frac{92.5}{100} \right) \]

### Step 4: Set Up the Equation
We know that the customer pays Rs. 2590 after both discounts:
\[ MP \times \left( \frac{87.5}{100} \right) \times \left( \frac{92.5}{100} \right) = 2590 \]

### Step 5: Simplify the Equation
Now, we can simplify the left side:
\[ MP \times \left( \frac{87.5 \times 92.5}{10000} \right) = 2590 \]

Calculating \( 87.5 \times 92.5 \):
\[ 87.5 \times 92.5 = 8093.75 \]
So, we have:
\[ MP \times \left( \frac{8093.75}{10000} \right) = 2590 \]

### Step 6: Solve for Marked Price (MP)
To find MP, we rearrange the equation:
\[ MP = \frac{2590 \times 10000}{8093.75} \]
Calculating the right side:
\[ MP = \frac{25900000}{8093.75} \approx 3200 \]

### Conclusion
The marked price of the cupboard is Rs. 3200.

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