Vishal goes to a shop to buy a radio costing Rs 2568. The rate of sales tax is 7%. He talks the shopkeeper to reduce the price of the radio to such an extent that he has to pay Rs 2568, inclusive of sales tax. Find the reduction needed in the price of the radio

Answer

To find the reduction needed in the price of the radio so that Vishal pays Rs 2568 inclusive of sales tax, we can follow these steps:

### Step 1: Understand the relationship between the selling price, cost price, and sales tax.
The selling price (SP) of an item that includes sales tax can be expressed as:
\[ SP = CP + (CP \times \text{Sales Tax Rate}) \]
Where:
- SP = Selling Price (inclusive of tax)
- CP = Cost Price (original price before tax)
- Sales Tax Rate = 7% = 0.07

### Step 2: Set up the equation.
Given that the selling price (SP) is Rs 2568, we can express this as:
\[ 2568 = CP + (CP \times 0.07) \]
This can be rewritten as:
\[ 2568 = CP \times (1 + 0.07) = CP \times 1.07 \]

### Step 3: Solve for the cost price (CP).
Now, we can solve for CP:
\[ CP = \frac{2568}{1.07} \]
Calculating this gives:
\[ CP = \frac{2568}{1.07} \approx 2400 \]

### Step 4: Calculate the original price of the radio.
The original price of the radio is Rs 2400.

### Step 5: Determine the reduction needed.
To find the reduction needed in the price of the radio, we subtract the new price (after the reduction) from the original price:
\[ \text{Reduction} = \text{Original Price} - \text{New Price} \]
\[ \text{Reduction} = 2400 - 2568 \]
Calculating this gives:
\[ \text{Reduction} = 2400 - 2568 = 168 \]

### Final Answer:
The reduction needed in the price of the radio is Rs 168.

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