The marked price of a dress is Rs.8610 which is 64% above the cost price. If the dress is sold at a profit of `26(2)/(3)%`, then find the difference between discount given and amount of profit earned (in Rs.)?

Options

A. `562.4`
B. `560`
C. `672`
D. `504`

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Find the Cost Price (CP)
Given that the marked price (MP) of the dress is Rs. 8610 and it is 64% above the cost price (CP), we can express this relationship mathematically.

The relationship can be written as:
\[ MP = CP + 0.64 \times CP \]
\[ MP = CP \times (1 + 0.64) \]
\[ MP = CP \times 1.64 \]

Now substituting the value of MP:
\[ 8610 = CP \times 1.64 \]

To find CP, we rearrange the equation:
\[ CP = \frac{8610}{1.64} \]

Calculating CP:
\[ CP = \frac{8610 \times 100}{164} \]
\[ CP = \frac{861000}{164} \]
\[ CP = 5250 \]

### Step 2: Calculate the Selling Price (SP)
The profit percentage is given as \( 26 \frac{2}{3} \% \), which can be converted to an improper fraction:
\[ 26 \frac{2}{3} = \frac{80}{3} \% \]

Now, we calculate the profit based on the cost price:
\[ \text{Profit} = \frac{80}{3} \% \text{ of } CP \]
\[ \text{Profit} = \frac{80}{300} \times 5250 \]
\[ \text{Profit} = \frac{80 \times 5250}{300} \]
\[ \text{Profit} = \frac{420000}{300} \]
\[ \text{Profit} = 1400 \]

Now, we can find the selling price (SP):
\[ SP = CP + \text{Profit} \]
\[ SP = 5250 + 1400 \]
\[ SP = 6650 \]

### Step 3: Calculate the Discount
The discount can be calculated as:
\[ \text{Discount} = MP - SP \]
\[ \text{Discount} = 8610 - 6650 \]
\[ \text{Discount} = 1960 \]

### Step 4: Find the Difference between Discount and Profit
Finally, we need to find the difference between the discount given and the profit earned:
\[ \text{Difference} = \text{Discount} - \text{Profit} \]
\[ \text{Difference} = 1960 - 1400 \]
\[ \text{Difference} = 560 \]

### Final Answer
The difference between the discount given and the amount of profit earned is Rs. 560.

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