The sum of three numbers is 300. If the ratio between first and second be 5:9 and that between second and third be 9:11, then second number is

Options

A. 12
B. 60
C. 108
D. 132

Answer

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

### Step 1: Define the Variables
Let the three numbers be represented as:
- First number = A
- Second number = B
- Third number = C

### Step 2: Set Up the Ratios
From the problem, we know:
- The ratio of the first number (A) to the second number (B) is 5:9.
- The ratio of the second number (B) to the third number (C) is 9:11.

We can express these ratios in terms of a common variable:
- Let A = 5x
- Let B = 9x
- Let C = (11/9)B = (11/9)(9x) = 11x

### Step 3: Write the Equation for the Sum
According to the problem, the sum of the three numbers is 300:
\[ A + B + C = 300 \]
Substituting the expressions we found:
\[ 5x + 9x + 11x = 300 \]

### Step 4: Combine Like Terms
Combine the terms on the left side:
\[ (5x + 9x + 11x) = 25x \]
Thus, we have:
\[ 25x = 300 \]

### Step 5: Solve for x
To find the value of x, divide both sides by 25:
\[ x = \frac{300}{25} \]
\[ x = 12 \]

### Step 6: Find the Second Number
Now that we have the value of x, we can find the second number (B):
\[ B = 9x = 9 \times 12 = 108 \]

### Conclusion
The second number is **108**.

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