Sunil noticed that `3/4` of a chocolate was already eaten. If he then eats `2/3` of what was remaining, then how much portion of the chocolate is left?

Options

A. `1/12`
B. `5/6`
C. `7/12`
D. `7/9`

Answer

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

### Step 1: Determine the total parts of the chocolate
The total chocolate can be considered as 1 whole, which can be represented as a fraction. Since Sunil noticed that \( \frac{3}{4} \) of the chocolate was already eaten, we can find out how much is left.

### Step 2: Calculate the remaining chocolate
If \( \frac{3}{4} \) is eaten, then the remaining portion of the chocolate is:
\[ 1 - \frac{3}{4} = \frac{1}{4} \]

### Step 3: Calculate how much Sunil eats from the remaining chocolate
Sunil then eats \( \frac{2}{3} \) of what is remaining. The remaining chocolate is \( \frac{1}{4} \). Therefore, the amount he eats is:
\[ \text{Amount eaten} = \frac{2}{3} \times \frac{1}{4} = \frac{2 \times 1}{3 \times 4} = \frac{2}{12} = \frac{1}{6} \]

### Step 4: Calculate the remaining chocolate after Sunil eats
Now, we need to find out how much chocolate is left after Sunil eats \( \frac{1}{6} \) of the total chocolate. We know that the total chocolate is 1 (or \( \frac{6}{6} \) for easier calculation):
\[ \text{Remaining chocolate} = \frac{1}{4} - \frac{1}{6} \]

### Step 5: Finding a common denominator
To subtract these fractions, we need a common denominator. The least common multiple of 4 and 6 is 12. We convert the fractions:
\[ \frac{1}{4} = \frac{3}{12} \quad \text{and} \quad \frac{1}{6} = \frac{2}{12} \]

### Step 6: Perform the subtraction
Now we can subtract:
\[ \text{Remaining chocolate} = \frac{3}{12} - \frac{2}{12} = \frac{1}{12} \]

### Final Answer
Thus, the portion of the chocolate that is left is:
\[ \frac{1}{12} \]