If `24` is `2/3` of `3/4` of a number, then what will be `1/4` of that number ?

Options

A. 8
B. 12
C. 10
D. 32

Answer

To solve the problem step by step, we will follow the instructions given in the video transcript.

### Step 1: Define the variable
Let the unknown number be represented as \( x \).

### Step 2: Set up the equation
According to the problem, \( 24 \) is \( \frac{2}{3} \) of \( \frac{3}{4} \) of \( x \). We can express this relationship as:
\[ 24 = \frac{2}{3} \times \frac{3}{4} \times x \]

### Step 3: Simplify the equation
First, simplify \( \frac{2}{3} \times \frac{3}{4} \):
\[ \frac{2}{3} \times \frac{3}{4} = \frac{2 \times 3}{3 \times 4} = \frac{6}{12} = \frac{1}{2} \]
Now, substitute this back into the equation:
\[ 24 = \frac{1}{2} \times x \]

### Step 4: Solve for \( x \)
To isolate \( x \), multiply both sides of the equation by \( 2 \):
\[ x = 24 \times 2 = 48 \]

### Step 5: Find \( \frac{1}{4} \) of \( x \)
Now that we have \( x = 48 \), we need to find \( \frac{1}{4} \) of \( x \):
\[ \frac{1}{4} \times 48 = 12 \]

### Final Answer
Thus, \( \frac{1}{4} \) of the number is \( 12 \).

---