If the price of 1kg of sugar is increased of `12(1)/(2)%` the increased is `Rs.58`. Find the original and new price ?

Options

A. `464, 522`
B. `465, 555`
C. `440, 520`
D. `475, 540`

Answer

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

### Step 1: Understand the percentage increase
The price of sugar has increased by \(12 \frac{1}{2}\%\). This can be converted to a fraction:
\[ 12 \frac{1}{2}\% = \frac{25}{2}\% = 0.125 \]

### Step 2: Set up the equation for the increase
Let the original price of sugar be \(x\). The increase in price can be expressed as:
\[ \text{Increase} = \frac{25}{2} \times \frac{x}{100} = \frac{25x}{200} = \frac{x}{8} \]
According to the problem, this increase is equal to Rs. 58:
\[ \frac{x}{8} = 58 \]

### Step 3: Solve for the original price \(x\)
To find \(x\), multiply both sides of the equation by 8:
\[ x = 58 \times 8 \]
Calculating this gives:
\[ x = 464 \]
So, the original price of sugar is Rs. 464.

### Step 4: Calculate the new price
The new price is the original price plus the increase:
\[ \text{New Price} = x + 58 = 464 + 58 = 522 \]

### Summary of Results
- **Original Price**: Rs. 464
- **New Price**: Rs. 522