The ratio of three numbers is `2 : 3:5`. If the sum of the three numbers is 275, then what is the largest among the three numbers?

Options

A. 142
B. 82.5
C. 137.5
D. 152

Answer

To solve the problem, we will follow these steps:

1. **Understand the Ratio**: The ratio of the three numbers is given as \(2 : 3 : 5\). This means we can express the three numbers in terms of a variable \(x\):
- Let the first number \(n_1 = 2x\)
- Let the second number \(n_2 = 3x\)
- Let the third number \(n_3 = 5x\)

2. **Set Up the Equation**: According to the problem, the sum of these three numbers is 275. Therefore, we can write the equation:
\[ n_1 + n_2 + n_3 = 275 \]
Substituting the expressions for \(n_1\), \(n_2\), and \(n_3\):
\[ 2x + 3x + 5x = 275 \]

3. **Combine Like Terms**: Now, combine the terms on the left side:
\[ (2x + 3x + 5x) = 10x \]
So the equation simplifies to:
\[ 10x = 275 \]

4. **Solve for \(x\)**: To find the value of \(x\), divide both sides of the equation by 10:
\[ x = \frac{275}{10} = 27.5 \]

5. **Find the Largest Number**: Now that we have the value of \(x\), we can find the largest number, which corresponds to \(n_3\):
\[ n_3 = 5x = 5 \times 27.5 = 137.5 \]

6. **Conclusion**: The largest among the three numbers is \(137.5\).