If b equals 10% of a and c equal 20% of b, then which one of the following equals 30% of c ?

Options

A. `0.0006%` of a
B. `0.006%` of
C. `0.06 %` of a
D. `0.6%` of a

Answer

To solve the problem step by step, we will follow the relationships given in the question:

1. **Understanding the relationships**:
- We know that \( b = 10\% \) of \( a \).
- We also know that \( c = 20\% \) of \( b \).

2. **Expressing \( b \) in terms of \( a \)**:
- Since \( b = 10\% \) of \( a \), we can write this as:
\[ b = \frac{10}{100} \times a = \frac{a}{10} \]

3. **Expressing \( c \) in terms of \( b \)**:
- Now, substituting \( b \) into the equation for \( c \):
\[ c = 20\% \text{ of } b = \frac{20}{100} \times b = \frac{1}{5} \times b \]
- Substituting \( b = \frac{a}{10} \) into the equation for \( c \):
\[ c = \frac{1}{5} \times \frac{a}{10} = \frac{a}{50} \]

4. **Finding \( 30\% \) of \( c \)**:
- Now we need to calculate \( 30\% \) of \( c \):
\[ 30\% \text{ of } c = \frac{30}{100} \times c = \frac{30}{100} \times \frac{a}{50} \]

5. **Simplifying the expression**:
- We can simplify this expression:
\[ = \frac{30a}{100 \times 50} = \frac{30a}{5000} \]
- This simplifies to:
\[ = \frac{a}{166.67} \]
- Alternatively, we can express it as:
\[ = a \times \frac{30}{5000} = a \times \frac{3}{500} = a \times 0.006 \]

6. **Expressing in percentage**:
- To express this in percentage:
\[ = 0.006 \times 100\% = 0.6\% \]

7. **Conclusion**:
- Therefore, \( 30\% \) of \( c \) equals \( 0.6\% \) of \( a \).

**Final Answer**: The correct option is \( 0.6\% \) of \( a \).