Calculating the Selling Price:

To find the amount for which the shopkeeper should have sold the DVD player to gain 12%, we need to first calculate the cost price of the DVD player.

Let's assume the cost price of the DVD player is 'x' rupees.

The shopkeeper sold the DVD player for 2816 rupees, which is 12% less than the cost price. This can be represented by the equation:

2816 = x - (12/100) * x

Simplifying this equation:

2816 = x - (0.12x)

Combining like terms:

2816 = 0.88x

Dividing both sides of the equation by 0.88:

x = 2816 / 0.88

x ≈ 3200

So, the cost price of the DVD player is approximately 3200 rupees.

Calculating the Selling Price to Gain 12%:

To find the amount for which the shopkeeper should have sold the DVD player to gain 12%, we can use the formula:

Selling Price = Cost Price + Profit

Given that the cost price is 3200 rupees and the desired profit is 12% of the cost price, we can calculate the selling price as follows:

Profit = (12/100) * 3200
= 384 rupees

Selling Price = Cost Price + Profit
= 3200 + 384
= 3584 rupees

Therefore, the shopkeeper should have sold the DVD player for 3584 rupees in order to gain a profit of 12%.

Summary:

- The shopkeeper sold the DVD player for 2816 rupees.
- To find the amount for which the shopkeeper should have sold the DVD player to gain 12%, we calculated the cost price of the DVD player.
- The cost price was found to be approximately 3200 rupees.
- Using the cost price and the desired profit of 12%, we calculated the selling price to be 3584 rupees.
- Hence, the shopkeeper should have sold the DVD player for 3584 rupees in order to gain a profit of 12%.

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