the price of sweater is increased by 8% if its increased price is ₹ 1566 find the original price

Answer

To find the original price of the sweater before the 8% increase, we can follow these steps:

### Step 1: Define the original price
Let the original price of the sweater be ₹x.

### Step 2: Calculate the increased price
An increase of 8% on the original price can be expressed mathematically as:
\[ \text{Increased Price} = \text{Original Price} + 8\% \text{ of Original Price} \]
This can be written as:
\[ \text{Increased Price} = x + \frac{8}{100} \times x \]
This simplifies to:
\[ \text{Increased Price} = x + 0.08x = 1.08x \]

### Step 3: Set up the equation
According to the problem, the increased price is ₹1566. Therefore, we can set up the equation:
\[ 1.08x = 1566 \]

### Step 4: Solve for x
To find the original price (x), divide both sides of the equation by 1.08:
\[ x = \frac{1566}{1.08} \]

### Step 5: Calculate the value
Now, we can perform the division:
\[ x = \frac{1566}{1.08} = 1450 \]

### Conclusion
Thus, the original price of the sweater is ₹1450.

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