Four numbers are in the ratio `1:2:3:4`. Their sum is 16. The sum of the first and fourth number is equal to :

Options

A. a) 5
B. b) 8
C. c) 10
D. d) 80

Answer

To solve the problem step by step, we will follow the reasoning outlined in the video transcript.

### Step 1: Understand the Ratio
The four numbers are in the ratio `1:2:3:4`. We can represent these numbers in terms of a variable \( x \):
- First number = \( x \)
- Second number = \( 2x \)
- Third number = \( 3x \)
- Fourth number = \( 4x \)

### Step 2: Set Up the Equation for the Sum
According to the problem, the sum of these four numbers is 16. Therefore, we can write the equation:
\[ x + 2x + 3x + 4x = 16 \]

### Step 3: Simplify the Equation
Combine the terms on the left side:
\[ 10x = 16 \]

### Step 4: Solve for \( x \)
To find the value of \( x \), divide both sides of the equation by 10:
\[ x = \frac{16}{10} = \frac{8}{5} \]

### Step 5: Find the First and Fourth Numbers
Now that we have the value of \( x \), we can find the first and fourth numbers:
- First number = \( x = \frac{8}{5} \)
- Fourth number = \( 4x = 4 \times \frac{8}{5} = \frac{32}{5} \)

### Step 6: Calculate the Sum of the First and Fourth Numbers
Now, we need to find the sum of the first and fourth numbers:
\[ \text{Sum} = x + 4x = \frac{8}{5} + \frac{32}{5} = \frac{40}{5} = 8 \]

### Final Answer
The sum of the first and fourth numbers is **8**.

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