The 1st, 2nd and 4th terms of a proportion are 12, 21 and 14 respectively. Its third term is

Options

A. 16
B. 18
C. 21
D. 8

Answer

To find the third term of the proportion where the first, second, and fourth terms are given as 12, 21, and 14 respectively, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Proportion**:
In a proportion, the ratio of the first term to the second term is equal to the ratio of the third term to the fourth term. This can be expressed as:
\[ \frac{\text{1st term}}{\text{2nd term}} = \frac{\text{3rd term}}{\text{4th term}} \]

2. **Substitute the Known Values**:
We know the values of the first, second, and fourth terms. Substitute these values into the proportion:
\[ \frac{12}{21} = \frac{x}{14} \]
Here, \( x \) represents the third term we need to find.

3. **Cross Multiply**:
To eliminate the fractions, we can cross-multiply:
\[ 12 \times 14 = 21 \times x \]

4. **Calculate the Left Side**:
Now calculate \( 12 \times 14 \):
\[ 12 \times 14 = 168 \]
So, we have:
\[ 168 = 21 \times x \]

5. **Solve for \( x \)**:
To find \( x \), divide both sides by 21:
\[ x = \frac{168}{21} \]

6. **Perform the Division**:
Now, calculate \( \frac{168}{21} \):
\[ x = 8 \]

7. **Conclusion**:
Therefore, the third term is:
\[ \text{Third term} = 8 \]