Final answer:
The marked price (MP) of the refrigerator is found by taking into account a 20% gain over the cost price (CP) of $11515 and a 16% discount off the marked price. By calculating the selling price (SP) based on the gain and expressing SP in terms of MP, we solve the equation to find MP to be $16450.
Step-by-step explanation:
To find the marked price of the refrigerator, we need to understand the concept of percentage profit and discounts. A dealer bought a refrigerator for $11515 and sells it after allowing a discount of 16% on its marked price but still gains 20% profit on the cost price.
Let's denote the marked price as 'MP'. A 16% discount on the marked price means the selling price (SP) is 84% of MP, so SP = 0.84 × MP. Since the dealer has a 20% gain, the cost price (CP) is related to the selling price (SP) by the equation SP = CP × (1 + gain%), which is SP = $11515 × (1 + 0.20).
We can set up the equation as follows:
- Calculate SP based on the gain: SP = $11515 × 1.20.
- Express SP in terms of MP: SP = 0.84 × MP.
- Equating both expressions for SP and solve for MP:
0.84 × MP = $11515 × 1.20
× MP = $11515 × 1.20 / 0.84
× MP = $16450
Therefore, the marked price of the refrigerator is $16450.