A reduction of `33(1)/3`% in the price of an item would enable a purchaser to get 4 more a rupee. No' of item price before reduction was :

Options

A. 2 per rupee
B. 4 per rupee
C. 12 per rupee
D. 8 per rupee

Answer

To solve the problem step by step, we will first understand the given information and then derive the required solution.

### Step 1: Understand the Reduction Percentage
The problem states that there is a reduction of \(33 \frac{1}{3}\%\) in the price of an item. This can be converted to a fraction:
\[ 33 \frac{1}{3}\% = \frac{33.33}{100} = \frac{1}{3} \]

### Step 2: Determine the Price After Reduction
If the original price of the item is \(P\), after a reduction of \(33 \frac{1}{3}\%\), the new price \(P'\) can be calculated as:
\[ P' = P - \frac{1}{3}P = \frac{2}{3}P \]

### Step 3: Understand the Effect of Price Reduction
According to the problem, after the price reduction, a purchaser can buy 4 more items for the same amount of money (1 rupee). This means that if the original price allowed the buyer to buy \(x\) items for 1 rupee, after the reduction, they can buy \(x + 4\) items for the same 1 rupee.

### Step 4: Set Up the Equation
The number of items that can be bought before the reduction is given by:
\[ x = \frac{1}{P} \]
After the reduction, the number of items that can be bought is:
\[ x + 4 = \frac{1}{P'} \]
Substituting \(P' = \frac{2}{3}P\) into the equation gives:
\[ x + 4 = \frac{1}{\frac{2}{3}P} = \frac{3}{2P} \]

### Step 5: Substitute the Value of \(x\)
Now substituting \(x = \frac{1}{P}\) into the equation:
\[ \frac{1}{P} + 4 = \frac{3}{2P} \]

### Step 6: Clear the Denominator
To eliminate the denominators, multiply through by \(2P\):
\[ 2 + 8P = 3 \]

### Step 7: Solve for \(P\)
Rearranging the equation gives:
\[ 8P = 3 - 2 \]
\[ 8P = 1 \]
\[ P = \frac{1}{8} \]

### Step 8: Calculate the Number of Items Before Reduction
The number of items that could be bought before the reduction is:
\[ x = \frac{1}{P} = \frac{1}{\frac{1}{8}} = 8 \]

### Final Answer
The number of items that could be bought before the reduction was **8 items per rupee**.

---