Calculating the TV Repair Cost

This problem involves calculating the cost of repairs for a second-hand TV, given the purchase price, selling price, and the profit percentage earned on the total cost.

Understanding the Variables

• Purchase Price of TV: ₹4,600
• Selling Price (SP): ₹5,406
• Profit Percentage: 6%
• Let the Repair Cost be $x$.
• Total Cost Price ($CP_{total}$) = Purchase Price + Repair Cost
• $CP_{total} = ₹4,600 + x$

Profit Calculation Logic

The profit is calculated based on the total cost price ($CP_{total}$). The formula relating Selling Price (SP), Total Cost Price ($CP_{total}$), and Profit Percentage is:

$SP = CP_{total} \times (1 + \text{Profit Rate})$

Here, the Profit Rate is 6% or 0.06.

Step-by-Step Calculation

1. Calculate the Total Cost Price ($CP_{total}$):

   Substitute the known values into the formula:

   $₹5,406 = CP_{total} \times (1 + 0.06)$

   $₹5,406 = CP_{total} \times 1.06$

   To find $CP_{total}$, divide the selling price by 1.06:

   $CP_{total} = \frac{₹5,406}{1.06}$

   $CP_{total} = ₹5,100$

2. Calculate the Repair Cost ($x$):

   The total cost price includes the original purchase price and the repair cost. Use the formula $CP_{total} = \text{Purchase Price} + \text{Repair Cost}$:

   $₹5,100 = ₹4,600 + x$

   Solve for $x$:

   $x = ₹5,100 - ₹4,600$

   $x = ₹500$

Conclusion

Rupert spent ₹500 on the repairs of the TV.