What is the fourth proportional of 18,24,30.

Options

A. 60
B. 89
C. 54
D. 40

Answer

To find the fourth proportional of the numbers 18, 24, and 30, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Concept of Fourth Proportional**:
The fourth proportional of three numbers \(a\), \(b\), and \(c\) is a number \(x\) such that the ratio of \(a\) to \(b\) is the same as the ratio of \(c\) to \(x\). Mathematically, this can be expressed as:
\[ \frac{a}{b} = \frac{c}{x} \]

2. **Assigning Values**:
Here, we have:
- \(a = 18\)
- \(b = 24\)
- \(c = 30\)
- We need to find \(x\).

3. **Setting Up the Equation**:
Using the relationship from step 1, we can set up the equation:
\[ \frac{18}{24} = \frac{30}{x} \]

4. **Cross Multiplying**:
Cross-multiply to eliminate the fractions:
\[ 18 \cdot x = 24 \cdot 30 \]

5. **Calculating the Right Side**:
Calculate \(24 \cdot 30\):
\[ 24 \cdot 30 = 720 \]
So, the equation now becomes:
\[ 18x = 720 \]

6. **Solving for \(x\)**:
To find \(x\), divide both sides by 18:
\[ x = \frac{720}{18} \]

7. **Performing the Division**:
Calculate \(720 \div 18\):
\[ 720 \div 18 = 40 \]

8. **Conclusion**:
Therefore, the fourth proportional of 18, 24, and 30 is:
\[ x = 40 \]

### Final Answer:
The fourth proportional is **40**.

---