Let the cost price of both the TV and the mobile phone be $xx$x.

Selling Price of the TV

The TV is sold at a profit of 12%, so its selling price can be expressed as:

$Selling Price (SP) of TV=Cost Price (CP)+12\mathrm{\%} of CP=x+0.12x=1.12x\backslash text\{Selling\; Price\; (SP)\; of\; TV\}\; =\; \backslash text\{Cost\; Price\; (CP)\}\; +\; 12\backslash \%\; \backslash text\{\; of\; CP\}\; =\; x\; +\; 0.12x\; =\; 1.12x$Selling Price (SP) of TV=Cost Price (CP)+12% of CP=x+0.12x=1.12x

Given that the selling price of the TV is ₹20,475, we have:

$1.12x=20,4751.12x\; =\; 20,475$1.12x=20,475

Now, solving for $xx$x:

$x=\frac{20,475}{1.12}=18,275 (Cost Price of TV and Mobile)x\; =\; \backslash frac\{20,475\}\{1.12\}\; =\; 18,275\; \backslash text\{\; (Cost\; Price\; of\; TV\; and\; Mobile)\}$x=1.1220,475​=18,275 (Cost Price of TV and Mobile)

Selling Price of the Mobile Phone

The mobile phone is sold at a loss of ₹1,456, so its selling price is:

$Selling Price (SP) of Mobile=x-1,456\backslash text\{Selling\; Price\; (SP)\; of\; Mobile\}\; =\; x\; –\; 1,456$Selling Price (SP) of Mobile=x−1,456

Substituting the value of $xx$x:

$SP of Mobile=18,275-1,456=16,819\backslash text\{SP\; of\; Mobile\}\; =\; 18,275\; –\; 1,456\; =\; 16,819$SP of Mobile=18,275−1,456=16,819

Total Cost Price and Selling Price

Now, we calculate the total cost price and total selling price:

$Total CP=x+x=2x=2\times 18,275=36,550\backslash text\{Total\; CP\}\; =\; x\; +\; x\; =\; 2x\; =\; 2\; \backslash times\; 18,275\; =\; 36,550$Total CP=x+x=2x=2×18,275=36,550 $Total SP=SP of TV+SP of Mobile=20,475+16,819=37,294\backslash text\{Total\; SP\}\; =\; \backslash text\{SP\; of\; TV\}\; +\; \backslash text\{SP\; of\; Mobile\}\; =\; 20,475\; +\; 16,819\; =\; 37,294$Total SP=SP of TV+SP of Mobile=20,475+16,819=37,294

Total Profit or Loss

Calculating the total profit:

$Total Profit=Total SP-Total CP=37,294-36,550=744\backslash text\{Total\; Profit\}\; =\; \backslash text\{Total\; SP\}\; –\; \backslash text\{Total\; CP\}\; =\; 37,294\; –\; 36,550\; =\; 744$Total Profit=Total SP−Total CP=37,294−36,550=744

Profit Percentage

Finally, calculating the profit percentage:

$Profit Percentage=\left(\frac{744}{36,550}\right)\times 100\approx 2.03\mathrm{\%}\backslash text\{Profit\; Percentage\}\; =\; \backslash left(\; \backslash frac\{744\}\{36,550\}\; \backslash right)\; \backslash times\; 100\; \backslash approx\; 2.03\backslash \%$Profit Percentage=(36,550744​)×100≈2.03%

Thus, the total percentage of profit in this business is approximately 2.03%.