The ratio between two numbers is 3:5 and their sum is 40. Find the larger of the two numbers.

Options

A. 15
B. 20
C. 25
D. 40

Explanation

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

### Step 1: Understand the Ratio
The ratio between two numbers is given as 3:5. This means that if we let the first number be represented as \(3x\) and the second number as \(5x\), where \(x\) is a common multiplier.

### Step 2: Set Up the Equation for the Sum
We know that the sum of the two numbers is 40. Therefore, we can write the equation:
\[ 3x + 5x = 40 \]

### Step 3: Combine Like Terms
Combine the terms on the left side of the equation:
\[ 8x = 40 \]

### Step 4: Solve for \(x\)
To find the value of \(x\), divide both sides of the equation by 8:
\[ x = \frac{40}{8} = 5 \]

### Step 5: Find the Two Numbers
Now that we have the value of \(x\), we can find the two numbers:
- The first number is \(3x = 3 \times 5 = 15\)
- The second number is \(5x = 5 \times 5 = 25\)

### Step 6: Identify the Larger Number
Now, we compare the two numbers:
- The first number is 15
- The second number is 25

The larger number is:
\[ \text{Larger number} = 25 \]

### Final Answer
The larger of the two numbers is **25**.

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