12:18::18:x
12/18= 18/x
12x= 18*18
12x= 324
x= 27
option (B)

The third proportional to 12 and 18 is:

To find the third proportional to two numbers, we need to set up a proportion and solve for the unknown value. In this case, we are given the numbers 12 and 18 and we need to find the third proportional.

Step 1: Set up the proportion
Let's assume the third proportional is x. We can set up the proportion as follows:

12 : 18 = 18 : x

Step 2: Cross-multiply and solve for x
Cross-multiplying the proportion gives us:

12 * x = 18 * 18

Simplifying the equation further:

12x = 324

Step 3: Solve for x
To solve for x, we divide both sides of the equation by 12:

x = 324 / 12

Simplifying the equation gives us:

x = 27

Therefore, the third proportional to 12 and 18 is 27.

Explanation:
To find the third proportional to two numbers, we can set up a proportion by comparing the ratios of the numbers. In this case, the ratio of 12 to 18 is the same as the ratio of 18 to the third proportional. By cross-multiplying and solving the equation, we find that the value of the third proportional is 27.

In simpler terms, if we have two numbers in a certain ratio, we can find the third number that is proportional to them by setting up a proportion and solving for the unknown value. This is a useful concept in mathematics and can be applied in various real-life scenarios, such as solving problems involving proportions or ratios.