When x is added to each of 10,23 15 and 33, the sums obtined in this order are in porpotion. The value of (x + 5) is ,

Options

A. 1
B. 8
C. 3
D. 5

Answer

To solve the problem step by step, we need to determine the value of \( x + 5 \) given that when \( x \) is added to each of the numbers 10, 23, 15, and 33, the resulting sums are in proportion.

### Step-by-Step Solution:

1. **Understanding Proportions**:
When we say that the sums are in proportion, we mean that:
\[ \frac{10 + x}{23 + x} = \frac{15 + x}{33 + x} \]

2. **Cross-Multiplying**:
To eliminate the fractions, we cross-multiply:
\[ (10 + x)(33 + x) = (23 + x)(15 + x) \]

3. **Expanding Both Sides**:
Now, we expand both sides of the equation:
- Left side:
\[ 10 \cdot 33 + 10x + 33x + x^2 = 330 + 43x + x^2 \]
- Right side:
\[ 23 \cdot 15 + 23x + 15x + x^2 = 345 + 38x + x^2 \]

4. **Setting the Equation**:
Now we set the two expanded sides equal to each other:
\[ 330 + 43x + x^2 = 345 + 38x + x^2 \]

5. **Cancelling \( x^2 \)**:
We can subtract \( x^2 \) from both sides:
\[ 330 + 43x = 345 + 38x \]

6. **Rearranging the Equation**:
Now, we rearrange the equation to isolate \( x \):
\[ 43x - 38x = 345 - 330 \]
This simplifies to:
\[ 5x = 15 \]

7. **Solving for \( x \)**:
Dividing both sides by 5 gives:
\[ x = 3 \]

8. **Finding \( x + 5 \)**:
Finally, we need to find \( x + 5 \):
\[ x + 5 = 3 + 5 = 8 \]

### Final Answer:
The value of \( x + 5 \) is \( 8 \).