The ratio of the marked price to the selling price of a smart camera is 7 : 6. The store owner earns a profit of 20% on the sale. If the difference between the marked price and the cost price of the camera is Rs. 400, find the selling price of the camera.

The correct answer is Rs. 1,200.

Step 1: Express Marked Price (MP) in terms of Selling Price (SP).

The ratio of Marked Price (MP) to Selling Price (SP) is given as 7 : 6.

$\frac{\mathrm{MP}}{\mathrm{SP}}=\frac{7}{6}$

Multiplying both sides by SP gives:

$\mathrm{MP}=\frac{7}{6}\mathrm{SP}$

Step 2: Express Cost Price (CP) in terms of Selling Price (SP).

The store owner earns a profit of 20% on the sale. Therefore, the relationship between Selling Price (SP) and Cost Price (CP) is:

$\mathrm{SP}=\mathrm{CP}+20\%\text{of}\mathrm{CP}$

$\mathrm{SP}=1.20\times \mathrm{CP}=\frac{6}{5}\mathrm{CP}$

Rearranging to solve for CP in terms of SP:

$\mathrm{CP}=\frac{5}{6}\mathrm{SP}$

Step 3: Calculate the Selling Price (SP).

We are given that the difference between the Marked Price and Cost Price is Rs. 400:

$\mathrm{MP}-\mathrm{CP}=400$

Substitute the expressions for MP and CP in terms of SP into the equation:

$\frac{7}{6}\mathrm{SP}-\frac{5}{6}\mathrm{SP}=400$

$\left(\frac{7}{6}-\frac{5}{6}\right)\mathrm{SP}=400$

$\frac{2}{6}\mathrm{SP}=400$

$\frac{1}{3}\mathrm{SP}=400$

$\mathrm{SP}=400\times 3$

$\mathrm{SP}=1200$

Thus, the selling price of the camera is Rs. 1,200.