40% of 250 is equal to 60% of what number?

Options

A. 150
B. 160
C. `166 2/3`
D. 270

Answer

To solve the problem "40% of 250 is equal to 60% of what number?", we can follow these steps:

### Step 1: Set up the equation
Let the unknown number be \( x \). According to the problem, we can express the relationship as:
\[ 40\% \text{ of } 250 = 60\% \text{ of } x \]
This can be written mathematically as:
\[ \frac{40}{100} \times 250 = \frac{60}{100} \times x \]

### Step 2: Simplify the percentages
We can simplify the percentages:
\[ \frac{40}{100} = 0.4 \quad \text{and} \quad \frac{60}{100} = 0.6 \]
Thus, the equation becomes:
\[ 0.4 \times 250 = 0.6 \times x \]

### Step 3: Calculate \( 40\% \) of \( 250 \)
Now, calculate \( 0.4 \times 250 \):
\[ 0.4 \times 250 = 100 \]
So, we have:
\[ 100 = 0.6 \times x \]

### Step 4: Solve for \( x \)
To find \( x \), we can rearrange the equation:
\[ x = \frac{100}{0.6} \]

### Step 5: Simplify the fraction
Now, simplify \( \frac{100}{0.6} \):
\[ x = \frac{1000}{6} = \frac{500}{3} \]

### Step 6: Convert to a mixed number
To convert \( \frac{500}{3} \) into a mixed number:
\[ 500 \div 3 = 166 \quad \text{remainder } 2 \]
So, \( \frac{500}{3} = 166 \frac{2}{3} \).

### Final Answer
Thus, the number \( x \) is:
\[ x = 166 \frac{2}{3} \]

### Conclusion
The correct option is option 3: \( 166 \frac{2}{3} \).

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