Shikha sells dinner sets at Rs 8,960. In a day she sells 8 sets and makes a profit of Rs 7,680. Find the cost price and the gain per cent of 1 dinner set.

Answer

To solve the problem step by step, we will find the cost price and the gain percentage of one dinner set sold by Shikha.

### Step 1: Find the Selling Price of One Dinner Set
Shikha sells dinner sets for a total of Rs 8,960. Since she sells 8 sets in a day, we can find the selling price of one set.

\[ \text{Selling Price (SP) of one set} = \frac{\text{Total Selling Price}}{\text{Number of Sets}} = \frac{8960}{8} = 1120 \]

### Step 2: Find the Profit on One Dinner Set
Shikha makes a total profit of Rs 7,680 from selling 8 sets. To find the profit on one set, we divide the total profit by the number of sets sold.

\[ \text{Profit on one set} = \frac{\text{Total Profit}}{\text{Number of Sets}} = \frac{7680}{8} = 960 \]

### Step 3: Find the Cost Price of One Dinner Set
The cost price (CP) can be calculated using the formula:

\[ \text{Cost Price (CP)} = \text{Selling Price (SP)} - \text{Profit} \]

Substituting the values we found:

\[ \text{CP of one set} = 1120 - 960 = 160 \]

### Step 4: Find the Gain Percentage
The gain percentage can be calculated using the formula:

\[ \text{Gain Percentage} = \left(\frac{\text{Profit}}{\text{Cost Price}} \times 100\right) \]

Substituting the values:

\[ \text{Gain Percentage} = \left(\frac{960}{8000} \times 100\right) = 12\% \]

### Final Answers
- Cost Price of one dinner set = Rs 8,000
- Gain Percentage = 12%