One-sixth of one-half of three-eighth of a number is 20. What will be 40% of that number?

Options

A. 256
B. 275
C. 286
D. 300

Answer

To solve the problem step by step, we start by defining the unknown number as \( x \).

### Step 1: Set up the equation
The problem states that one-sixth of one-half of three-eighths of a number is equal to 20. We can express this mathematically as:
\[ \frac{1}{6} \times \frac{1}{2} \times \frac{3}{8} \times x = 20 \]

### Step 2: Simplify the left side of the equation
Now, we simplify the left side of the equation:
\[ \frac{1 \times 1 \times 3}{6 \times 2 \times 8} \times x = 20 \]
Calculating the denominator:
\[ 6 \times 2 = 12 \]
\[ 12 \times 8 = 96 \]
So, we have:
\[ \frac{3}{96} \times x = 20 \]

### Step 3: Simplify the fraction
Next, we simplify \(\frac{3}{96}\):
\[ \frac{3}{96} = \frac{1}{32} \]
Thus, the equation becomes:
\[ \frac{1}{32} \times x = 20 \]

### Step 4: Solve for \( x \)
To find \( x \), we multiply both sides of the equation by 32:
\[ x = 20 \times 32 \]
Calculating the right side:
\[ 20 \times 32 = 640 \]
So, \( x = 640 \).

### Step 5: Calculate 40% of \( x \)
Now, we need to find 40% of the number \( x \):
\[ 40\% \text{ of } x = \frac{40}{100} \times 640 \]
This simplifies to:
\[ 0.4 \times 640 \]
Calculating:
\[ 0.4 \times 640 = 256 \]

### Final Answer
Thus, 40% of that number is:
\[ \boxed{256} \]