The ratio between two numbers is 7 : 16. If the second numberis 256 then the first number is:

Options

A. 120
B. 156
C. 112
D. 144

Answer

To solve the problem step by step, we can follow these instructions:

1. **Understand the Ratio**: The ratio of the two numbers is given as 7:16. This means that if the first number is represented as \( x \), then the second number can be represented as \( \frac{16}{7}x \).

2. **Set Up the Equation**: We know the second number is 256. Therefore, we can set up the equation:
\[ \frac{16}{7}x = 256 \]

3. **Solve for \( x \)**: To find \( x \), we can rearrange the equation:
\[ x = \frac{256 \times 7}{16} \]

4. **Calculate the Value**: Now, we will perform the multiplication and division:
- First, calculate \( 256 \div 16 \):
\[ 256 \div 16 = 16 \]
- Next, multiply by 7:
\[ 16 \times 7 = 112 \]

5. **Conclusion**: Therefore, the first number \( x \) is 112.

Final answer: The first number is **112**.