3/4th of 2/3rd of 1/5th of a number is 249.6. What is 50% of that number?

Options

A. a. 3794
B. b. 3749
C. c. 3734
D. d. none of these

Answer

To solve the problem step by step, we can follow these instructions:

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

### Step 2: Set up the equation
According to the problem, we have:
\[ \frac{3}{4} \text{ of } \frac{2}{3} \text{ of } \frac{1}{5} \text{ of } x = 249.6 \]
This can be written mathematically as:
\[ \frac{3}{4} \times \frac{2}{3} \times \frac{1}{5} \times x = 249.6 \]

### Step 3: Simplify the left side
Now, we simplify the left side of the equation:
\[ \frac{3 \times 2 \times 1}{4 \times 3 \times 5} \times x = 249.6 \]
The \( 3 \) in the numerator and denominator cancels out:
\[ \frac{2}{4 \times 5} \times x = 249.6 \]
This simplifies to:
\[ \frac{1}{10} \times x = 249.6 \]

### Step 4: Solve for \( x \)
Now, to isolate \( x \), multiply both sides by \( 10 \):
\[ x = 249.6 \times 10 \]
Calculating this gives:
\[ x = 2496 \]

### Step 5: Calculate 50% of \( x \)
Now, we need to find 50% of \( x \):
\[ 50\% \text{ of } x = \frac{50}{100} \times 2496 = \frac{1}{2} \times 2496 \]
Calculating this gives:
\[ 50\% \text{ of } 2496 = 1248 \]

### Final Answer
Thus, 50% of the number is:
\[ \boxed{1248} \]

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