A television manufacturer earns a profit of 10% by selling one TV set for ₹24,750. If the production cost is increased by 15%, then what should be the new selling price of the TV set so as to gain a profit of 15%?

Current Selling Price = ₹24,750

Profit Percentage (Initial) = 10%

Production Cost Increase = 15%

Desired Profit Percentage = 15%

​$$\text{Cost Price (CP)} = \frac{\text{Selling Price (SP)}}{1 + \frac{\text{Profit Percentage}}{100}}$$  ​

Calculating the original cost price (CP).

​$$\text{CP} = \frac{24,750}{1 + \frac{10}{100}} = \frac{24,750}{1.10} = ₹22,500$$ ​

Calculating the new cost price after a 15% increase:

​$$\text{New CP} = ₹22,500 \times \left(1 + \frac{15}{100}\right) = ₹22,500 \times 1.15 = ₹25,875 \\$$​​

Now, calculating the new selling price to achieve a 15% profit:

​$$\text{New SP} = ₹25,875 \times \left(1 + \frac{15}{100}\right) = ₹25,875 \times 1.15 = ₹29,756.25 \\$$  ​

Thus, the new selling price of the TV set should be ₹29,756.25.