If `3/5`th part of 60% of a number is 36, then that number is

Options

A. 100
B. 75
C. 80
D. 90

Answer

To solve the problem, we need to find the number \( x \) such that \( \frac{3}{5} \) of \( 60\% \) of \( x \) equals \( 36 \).

### Step-by-step Solution:

1. **Understand the problem**: We need to express the given condition mathematically. We know that \( \frac{3}{5} \) of \( 60\% \) of a number \( x \) is equal to \( 36 \).

2. **Convert percentages to fractions**:
\[ 60\% = \frac{60}{100} = \frac{3}{5} \]

3. **Set up the equation**:
\[ \frac{3}{5} \times \left(\frac{3}{5} \times x\right) = 36 \]

4. **Simplify the left side**:
\[ \frac{3}{5} \times \frac{3}{5} \times x = \frac{9}{25} x \]
So, we can rewrite the equation as:
\[ \frac{9}{25} x = 36 \]

5. **Isolate \( x \)**: To find \( x \), we can multiply both sides by the reciprocal of \( \frac{9}{25} \):
\[ x = 36 \times \frac{25}{9} \]

6. **Calculate the right side**:
\[ x = 36 \times \frac{25}{9} = \frac{36 \times 25}{9} \]

7. **Simplify the fraction**:
\[ 36 \div 9 = 4 \quad \text{(so we can simplify)} \]
Thus,
\[ x = 4 \times 25 = 100 \]

### Final Answer:
The number \( x \) is \( 100 \).