A music system when sold for Rs.4500 gives a loss of 16.66% to the merchant who sells it. Calculate his loss or gain per cent, if he sells it for Rs.5703.75.

Step 1: First, we need to find the cost price of the music system. We know that when the music system is sold for Rs.4500, the merchant incurs a loss of 16.66%. This means that Rs.4500 is 83.34% (100% - 16.66%) of the cost price.

So, we can set up the equation: 4500 = 83.34/100 * Cost price

Solving for Cost price gives us: Cost price = 4500 / (83.34/100) = Rs.5400

Step 2: Next, we need to find out the gain or loss when the music system is sold for Rs.5703.75.

The gain is calculated as: Gain = Selling price - Cost price = 5703.75 - 5400 = Rs.303.75

Step 3: Finally, we need to calculate the gain percentage. The gain percentage is calculated as: Gain % = (Gain / Cost price) * 100 = (303.75 / 5400) * 100 = 5.625%

So, the merchant has a gain of 5.625% when he sells the music system for Rs.5703.75.