If 70% of `5//7^(th)` of a number is 90 , find the number .

Options

A. 150
B. 180
C. 160
D. 190

Answer

To solve the problem step by step, we will follow the mathematical operations as described in the video transcript.

### Step-by-Step Solution:

1. **Let the Number be A**:
We start by letting the unknown number be represented by the variable \( A \).

2. **Set Up the Equation**:
According to the problem, we know that 70% of \( \frac{5}{7} \) of \( A \) equals 90. We can express this mathematically as:
\[ \frac{70}{100} \times \frac{5}{7} \times A = 90 \]

3. **Simplify the Equation**:
We can simplify \( \frac{70}{100} \) to \( 0.7 \) or \( \frac{7}{10} \). Thus, the equation becomes:
\[ \frac{7}{10} \times \frac{5}{7} \times A = 90 \]

4. **Multiply the Fractions**:
Now, we can multiply \( \frac{7}{10} \) and \( \frac{5}{7} \):
\[ \frac{7 \times 5}{10 \times 7} \times A = 90 \]
The \( 7 \) in the numerator and denominator cancels out:
\[ \frac{5}{10} \times A = 90 \]

5. **Further Simplify**:
\( \frac{5}{10} \) simplifies to \( \frac{1}{2} \):
\[ \frac{1}{2} \times A = 90 \]

6. **Solve for A**:
To find \( A \), multiply both sides of the equation by 2:
\[ A = 90 \times 2 \]
\[ A = 180 \]

7. **Conclusion**:
The number \( A \) is 180.

### Final Answer:
The number is **180**.