List price of a cooler is Rs 2563. The rate of VAT is 10%. The customer requests the shopkeeper to allow a discount in the price of the cooler to such an extent that the price remains Rs 2563 inclusive  of  VAT. Find the discount in the price of the cooler.

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the Problem
We need to find the discount on a cooler whose list price is Rs 2563, and the VAT is 10%. The final price after applying VAT must remain Rs 2563.

### Step 2: Define the Variables
Let the reduced price of the cooler (excluding VAT) be Rs X.

### Step 3: Calculate the VAT Amount
The VAT is 10% of the reduced price (X). Therefore, the VAT amount can be expressed as:
\[ \text{VAT} = 10\% \text{ of } X = \frac{10}{100} \times X = \frac{X}{10} \]

### Step 4: Write the Selling Price Equation
The selling price (inclusive of VAT) can be expressed as:
\[ \text{Selling Price} = \text{Reduced Price} + \text{VAT} = X + \frac{X}{10} \]
To combine these, we find a common denominator:
\[ \text{Selling Price} = X + \frac{X}{10} = \frac{10X}{10} + \frac{X}{10} = \frac{11X}{10} \]

### Step 5: Set Up the Equation
Since the selling price is given as Rs 2563, we can set up the equation:
\[ \frac{11X}{10} = 2563 \]

### Step 6: Solve for X
To find X, we multiply both sides by 10:
\[ 11X = 2563 \times 10 \]
\[ 11X = 25630 \]
Now, divide both sides by 11:
\[ X = \frac{25630}{11} = 2330 \]

### Step 7: Calculate the Discount
The discount allowed is the difference between the list price and the reduced price:
\[ \text{Discount} = \text{List Price} - \text{Reduced Price} = 2563 - 2330 \]
\[ \text{Discount} = 233 \]

### Final Answer
The discount allowed on the cooler is Rs 233.

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