If the price of an item is increased by 30% and then allows two successive discounts of 10% and 10%. In last the price of an item is

Options

A. increased by 10%
B. increased by 5.3%
C. decreased by 3%
D. decreased by 5.3%

Answer

Let's solve the problem step by step.

### Step 1: Determine the Original Price
Let the original price of the item be \( P = 100 \).

### Step 2: Calculate the Increased Price
The price is increased by 30%. To find the increased price, we calculate:
\[ \text{Increased Price} = P + (30\% \text{ of } P) = 100 + (0.30 \times 100) = 100 + 30 = 130 \]

### Step 3: Apply the First Discount
Now, we apply the first discount of 10% on the increased price of 130:
\[ \text{First Discount Amount} = 10\% \text{ of } 130 = 0.10 \times 130 = 13 \]
So, the price after the first discount is:
\[ \text{Price after First Discount} = 130 - 13 = 117 \]

### Step 4: Apply the Second Discount
Next, we apply the second discount of 10% on the new price of 117:
\[ \text{Second Discount Amount} = 10\% \text{ of } 117 = 0.10 \times 117 = 11.7 \]
Thus, the final price after the second discount is:
\[ \text{Final Price} = 117 - 11.7 = 105.3 \]

### Final Answer
The final price of the item after the price increase and two successive discounts is **105.3**.

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