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

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Understand the total payment including sales tax
Vishal wants to pay Rs. 2568, which includes a sales tax of 7%. This means that the price before tax (let's call it the cost price, CP) plus the sales tax should equal Rs. 2568.

### Step 2: Set up the equation
Let the cost price (CP) be represented as \( x \). The sales tax can be calculated as 7% of \( x \), which is \( 0.07x \). Therefore, the total amount paid can be expressed as:
\[ x + 0.07x = 2568 \]
This simplifies to:
\[ 1.07x = 2568 \]

### Step 3: Solve for the cost price (CP)
To find \( x \), we can rearrange the equation:
\[ x = \frac{2568}{1.07} \]
Calculating this gives:
\[ x = 2400 \]

### Step 4: Calculate the reduction in price
The original price of the radio was Rs. 2568, and the new price (cost price after reduction) is Rs. 2400. To find the reduction needed, we subtract the new price from the original price:
\[ \text{Reduction} = 2568 - 2400 \]
Calculating this gives:
\[ \text{Reduction} = 168 \]

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

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