Rs 1,680
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.
The shop wants a 12% profit on the cost price.
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 = $1,260 \times (1 + \frac{12}{100}) = 1,260 \times 1.12 = ₹ 1,411.20$
A discount of 16% is allowed on the marked price. This means the selling price is 84% of the marked price (100% - 16% = 84%).
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
The antique shop should mark the price at ₹ 1,680 to achieve a 12% gain after allowing a 16% discount.