Shopkeeper give discount of 23% on marked price of a toy and gets Rs 56 profit. If this profit percentage is 10% then determine the marked price of that toy?

Options

A. Rs 810
B. Rs 800
C. Rs 560
D. Rs 740

Answer

To determine the marked price of the toy, we can follow these steps:

### Step 1: Understand the given information
- Discount = 23% on the marked price (MP)
- Profit = Rs. 56
- Profit percentage = 10%

### Step 2: Set up the equations
Let the marked price (MP) be \( x \).

The selling price (SP) after applying the discount can be calculated as:
\[ SP = MP - (23\% \text{ of } MP) = x - 0.23x = 0.77x \]

### Step 3: Relate profit and cost price (CP)
We know that profit is given by:
\[ \text{Profit} = SP - CP \]
Given that the profit is Rs. 56, we can write:
\[ 56 = SP - CP \]

### Step 4: Express CP in terms of SP
We also know that profit percentage is given by:
\[ \text{Profit Percentage} = \frac{\text{Profit}}{CP} \times 100 \]
Given that the profit percentage is 10%, we can express this as:
\[ 10 = \frac{56}{CP} \times 100 \]
From this, we find:
\[ CP = \frac{56 \times 100}{10} = 560 \]

### Step 5: Substitute CP into the profit equation
Now, substituting CP back into the profit equation:
\[ 56 = SP - 560 \]
Thus, we can find SP:
\[ SP = 56 + 560 = 616 \]

### Step 6: Relate SP back to MP
We have already established that:
\[ SP = 0.77x \]
So, substituting for SP:
\[ 616 = 0.77x \]

### Step 7: Solve for x (the marked price)
To find the marked price (MP), we rearrange the equation:
\[ x = \frac{616}{0.77} \]
Calculating this gives:
\[ x = 800 \]

### Conclusion
The marked price of the toy is Rs. 800.

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