Anjuli bought some chocolates from Nestle's exclusive shop, she gave to Amit one less than half of what she had initially. Then she had given 3 chocolates to Bablu and then half of the chocolates which she had then given to charles. Thus finally she gave one chocolate to Deepak and the remaining one she ate herself. The number of chocolates she had purchased.

Options

A. a. 9
B. b. 12
C. c. 10
D. d. 15

Answer

To solve the problem step by step, we will define the variables and break down the actions Anjuli took with the chocolates.

### Step 1: Define the initial amount of chocolates
Let \( X \) be the total number of chocolates Anjuli initially bought.

### Step 2: Calculate the chocolates given to Amit
Anjuli gave Amit one less than half of what she had initially. This can be expressed as:
\[ \text{Chocolates given to Amit} = \frac{X}{2} - 1 \]

### Step 3: Calculate the remaining chocolates after giving to Amit
After giving chocolates to Amit, the number of chocolates Anjuli has left is:
\[ \text{Remaining chocolates} = X - \left(\frac{X}{2} - 1\right) = X - \frac{X}{2} + 1 = \frac{X}{2} + 1 \]

### Step 4: Calculate the chocolates given to Bablu
Anjuli then gave 3 chocolates to Bablu. The number of chocolates left after this is:
\[ \text{Remaining chocolates after Bablu} = \left(\frac{X}{2} + 1\right) - 3 = \frac{X}{2} - 2 \]

### Step 5: Calculate the chocolates given to Charles
Next, Anjuli gave half of the remaining chocolates to Charles:
\[ \text{Chocolates given to Charles} = \frac{1}{2} \left(\frac{X}{2} - 2\right) = \frac{X}{4} - 1 \]
The remaining chocolates after giving to Charles are:
\[ \text{Remaining chocolates after Charles} = \left(\frac{X}{2} - 2\right) - \left(\frac{X}{4} - 1\right) = \frac{X}{2} - 2 - \frac{X}{4} + 1 = \frac{X}{4} - 1 \]

### Step 6: Calculate the chocolates given to Deepak
Anjuli then gave 1 chocolate to Deepak. The remaining chocolates after this are:
\[ \text{Remaining chocolates after Deepak} = \left(\frac{X}{4} - 1\right) - 1 = \frac{X}{4} - 2 \]

### Step 7: Determine the final condition
According to the problem, Anjuli ate the last remaining chocolate, which means:
\[ \frac{X}{4} - 2 = 1 \]

### Step 8: Solve for \( X \)
Now we solve the equation:
\[ \frac{X}{4} - 2 = 1 \]
Adding 2 to both sides:
\[ \frac{X}{4} = 3 \]
Multiplying both sides by 4:
\[ X = 12 \]

### Conclusion
The total number of chocolates Anjuli initially purchased is \( \boxed{12} \).

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