Let's solve this problem step-by-step:
1. Find the Original VAT Amount:
- The marked price of the air-conditioner is ₹ 30,500.
- The VAT percentage is 12%.
To calculate the VAT amount:
[tex]\[
\text{VAT amount} = \text{marked price} \times \left(\frac{\text{VAT percentage}}{100}\right)
\][/tex]
[tex]\[
\text{VAT amount} = ₹ 30,500 \times \left(\frac{12}{100}\right) = ₹ 30,500 \times 0.12 = ₹ 3,660
\][/tex]
2. Calculate the Initial Final Price Including VAT:
- The initial final price is the marked price plus the VAT amount.
[tex]\[
\text{Initial final price} = \text{marked price} + \text{VAT amount}
\][/tex]
[tex]\[
\text{Initial final price} = ₹ 30,500 + ₹ 3,660 = ₹ 34,160
\][/tex]
3. Determine the Bargained Final Price:
- After bargaining, Savita agrees to pay ₹ 30,500 including VAT.
This means the effective final price after bargaining is ₹ 30,500.
4. Calculate the Reduction by the Shopkeeper:
- The amount reduced by the shopkeeper is the difference between the initial final price (including VAT) and the bargained final price.
[tex]\[
\text{Amount reduced} = \text{Initial final price} - \text{Bargained final price}
\][/tex]
[tex]\[
\text{Amount reduced} = ₹ 34,160 - ₹ 30,500 = ₹ 3,660
\][/tex]
So, the amount reduced by the shopkeeper is ₹ 3,660.
Thus, the answer to the question is that the shopkeeper reduced the amount by [tex]\( S = ₹ 3,660 \)[/tex].
