Antique Pricing Strategy: Calculating Marked Price

To determine the marked price (MP) for the antique piece, we need to consider the cost price (CP), the desired profit, and the allowed discount.

1. Calculate the Selling Price (SP)

The shop wants a 12% profit on the cost price.

• Cost Price (CP) = ₹ 1,260
• Profit Percentage = 12%
• Profit Amount = 12% of ₹ 1,260

Using the formula for profit amount:

Profit Amount = $CP \times \frac{\text{Profit Percentage}}{100}$

Profit Amount = $1,260 \times \frac{12}{100} = 1,260 \times 0.12 = ₹ 151.20$

The Selling Price (SP) is the cost price plus the profit.

SP = CP + Profit Amount

SP = $1,260 + 151.20 = ₹ 1,411.20$

Alternatively, calculate SP directly:

SP = $CP \times (1 + \frac{\text{Profit Percentage}}{100})$

SP = $1,260 \times (1 + \frac{12}{100}) = 1,260 \times 1.12 = ₹ 1,411.20$

2. Calculate the Marked Price (MP)

A discount of 16% is allowed on the marked price. This means the selling price is 84% of the marked price (100% - 16% = 84%).

• Selling Price (SP) = ₹ 1,411.20
• Discount Percentage = 16%
• SP = MP $\times (1 - \frac{\text{Discount Percentage}}{100})$

Substitute the known values:

$1,411.20 = MP \times (1 - \frac{16}{100})$

$1,411.20 = MP \times (1 - 0.16)$

$1,411.20 = MP \times 0.84$

Now, solve for MP:

MP = $\frac{1,411.20}{0.84}$

MP = ₹ 1,680

Conclusion

The antique shop should mark the price at ₹ 1,680 to achieve a 12% gain after allowing a 16% discount.