What number should be added to each of the numbers 94, 24, 100 and 26, so that the resulting numbers are In continued proportion?

Options

A. 10
B. 11
C. 9
D. 8

Answer

To solve the problem of finding the number that should be added to each of the numbers 94, 24, 100, and 26 so that the resulting numbers are in continued proportion, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Continued Proportion**:
For four numbers \(a\), \(b\), \(c\), and \(d\) to be in continued proportion, the relationship can be expressed as:
\[ \frac{a}{b} = \frac{c}{d} \]
In our case, we need to find a number \(x\) such that:
\[ \frac{94 + x}{24 + x} = \frac{100 + x}{26 + x} \]

2. **Cross-Multiplying**:
To eliminate the fractions, we cross-multiply:
\[ (94 + x)(26 + x) = (24 + x)(100 + x) \]

3. **Expanding Both Sides**:
Now, we expand both sides of the equation:
- Left Side:
\[ 94 \cdot 26 + 94x + 26x + x^2 = 2444 + 120x + x^2 \]
- Right Side:
\[ 24 \cdot 100 + 24x + 100x + x^2 = 2400 + 124x + x^2 \]

4. **Setting the Equation**:
Now we set the expanded forms equal to each other:
\[ 2444 + 120x + x^2 = 2400 + 124x + x^2 \]

5. **Simplifying the Equation**:
We can cancel \(x^2\) from both sides:
\[ 2444 + 120x = 2400 + 124x \]
Rearranging gives:
\[ 2444 - 2400 = 124x - 120x \]
Simplifying further:
\[ 44 = 4x \]

6. **Solving for \(x\)**:
Dividing both sides by 4:
\[ x = \frac{44}{4} = 11 \]

### Conclusion:
The number that should be added to each of the numbers 94, 24, 100, and 26 is **11**.