If 25% of two-third of a number is 10, what is the number?

Options

A. 40
B. 20
C. 60
D. 30

Answer

To solve the problem, we need to find the number \( x \) such that 25% of two-thirds of \( x \) equals 10. Let's break this down step by step.

### Step 1: Set up the equation
We know that 25% can be expressed as a fraction:
\[ 25\% = \frac{25}{100} = \frac{1}{4} \]
Two-thirds of \( x \) can be expressed as:
\[ \frac{2}{3}x \]
Thus, we can write the equation:
\[ \frac{1}{4} \times \frac{2}{3}x = 10 \]

### Step 2: Simplify the left side of the equation
Now, we can simplify the left side of the equation:
\[ \frac{1}{4} \times \frac{2}{3}x = \frac{2}{12}x = \frac{1}{6}x \]
So, our equation now looks like:
\[ \frac{1}{6}x = 10 \]

### Step 3: Solve for \( x \)
To isolate \( x \), we can multiply both sides of the equation by 6:
\[ x = 10 \times 6 \]
\[ x = 60 \]

### Conclusion
The number is \( 60 \).