A man sells chocolate which are in the boxes. Only either full box or half a box of chocolate can be purchased from him. A customer comes and buys half the number of boxes which the seller had plus half a box more. A second customer comes and purchases half the remaining number of boxes plus half a box. After this the seller is left with no chocolate boxes. How many chocolate boxes the seller had initially ?

Options

A. 2
B. 3
C. 4
D. 3.5

Answer

To solve the problem step by step, let's denote the initial number of boxes the seller had as \( x \).

### Step 1: First Customer's Purchase
The first customer buys half the number of boxes the seller had plus half a box more. This can be expressed mathematically as:
\[ \text{Boxes bought by first customer} = \frac{x}{2} + \frac{1}{2} \]
After this purchase, the number of boxes left with the seller becomes:
\[ \text{Remaining boxes} = x - \left(\frac{x}{2} + \frac{1}{2}\right) = x - \frac{x}{2} - \frac{1}{2} = \frac{x}{2} - \frac{1}{2} \]

### Step 2: Second Customer's Purchase
The second customer then comes and buys half of the remaining boxes plus half a box. The remaining boxes after the first customer is \( \frac{x}{2} - \frac{1}{2} \). The second customer buys:
\[ \text{Boxes bought by second customer} = \frac{1}{2} \left(\frac{x}{2} - \frac{1}{2}\right) + \frac{1}{2} \]
Calculating this:
\[ = \frac{x}{4} - \frac{1}{4} + \frac{1}{2} = \frac{x}{4} - \frac{1}{4} + \frac{2}{4} = \frac{x}{4} + \frac{1}{4} \]
After this purchase, the number of boxes left with the seller becomes:
\[ \text{Remaining boxes} = \left(\frac{x}{2} - \frac{1}{2}\right) - \left(\frac{x}{4} + \frac{1}{4}\right) \]
Calculating this:
\[ = \frac{x}{2} - \frac{1}{2} - \frac{x}{4} - \frac{1}{4} = \frac{2x}{4} - \frac{x}{4} - \frac{2}{4} - \frac{1}{4} = \frac{x}{4} - \frac{3}{4} \]

### Step 3: Setting the Equation
According to the problem, after both customers, the seller is left with no boxes:
\[ \frac{x}{4} - \frac{3}{4} = 0 \]
Solving for \( x \):
\[ \frac{x}{4} = \frac{3}{4} \]
Multiplying both sides by 4:
\[ x = 3 \]

### Conclusion
The seller initially had **3 boxes** of chocolates.