Three of the four parts are exactly equal. Which of the parts is not equal to other three ?

Options

A. `20%` of `40%` of `50`
B. `60%` of `50`
C. `100/3%` of `90`
D. none of these

Answer

To solve the problem, we need to determine which of the four parts is not equal to the other three. We will analyze each option step by step.

### Step-by-Step Solution:

1. **Identify the Options**: We have four options to evaluate. Let's denote them as:
- Option 1: \(20\% \text{ of } 40\% \text{ of } 50\)
- Option 2: \(60\% \text{ of } 50\)
- Option 3: \( \frac{100}{3}\% \text{ of } 90\)
- Option 4: None of these

2. **Calculate Option 1**:
- \(20\% \text{ of } 40\% \text{ of } 50\)
- Convert percentages to fractions:
\[ 20\% = \frac{20}{100} = \frac{1}{5}, \quad 40\% = \frac{40}{100} = \frac{2}{5} \]
- Calculate:
\[ \frac{1}{5} \times \frac{2}{5} \times 50 = \frac{1 \times 2 \times 50}{5 \times 5} = \frac{100}{25} = 4 \]

3. **Calculate Option 2**:
- \(60\% \text{ of } 50\)
- Convert percentage to fraction:
\[ 60\% = \frac{60}{100} = \frac{3}{5} \]
- Calculate:
\[ \frac{3}{5} \times 50 = \frac{3 \times 50}{5} = \frac{150}{5} = 30 \]

4. **Calculate Option 3**:
- \( \frac{100}{3}\% \text{ of } 90\)
- Convert percentage to fraction:
\[ \frac{100}{3}\% = \frac{100}{3} \times \frac{1}{100} = \frac{1}{3} \]
- Calculate:
\[ \frac{1}{3} \times 90 = \frac{90}{3} = 30 \]

5. **Compare the Results**:
- Option 1: 4
- Option 2: 30
- Option 3: 30
- Option 4: None of these

6. **Conclusion**:
- The first option (4) is not equal to the other three options (30, 30). Therefore, the part that is not equal to the other three is **Option 1**.

### Final Answer:
The part that is not equal to the other three is **Option 1**.