Given: Mode = 18, Mean = 24

To find: Median

Formula to find Median:
For odd number of observations, Median = value of (n+1)/2th observation in the ordered data set
For even number of observations, Median = average of value of n/2th and (n/2 + 1)th observation in the ordered data set

Let's assume a data set with 5 observations, and the mode is 18. Since mode is the most frequent value in the data set, we can assume that there are two observations with value 18. Let's arrange the data set in ascending order:

18, 18, a, b, c

The mean of the data set is 24. We know that the sum of all observations in the data set divided by the number of observations gives the mean. Therefore, we can write:

(18 + 18 + a + b + c)/5 = 24

Simplifying the equation, we get:

a + b + c = 66

Now, we can use the formula to find the median. Since there are 5 observations in the data set, the median is the value of the 3rd observation, which is 'a'.

To find 'a', we need to use the fact that there are two observations with value 18. Let's consider two cases:

Case 1: If 'a' is also 18
In this case, the data set would be:

18, 18, 18, b, c

Using the equation a + b + c = 66, we get:

54 + b + c = 66

b + c = 12

The median would be the value of the 3rd observation, which is 18.

However, the mode of this data set would be 18, which contradicts the given information that the mode is 18. Therefore, we can discard this case.

Case 2: If 'a' is not 18
In this case, the data set would be:

18, 18, a, b, c

Using the equation a + b + c = 66, we get:

36 + b + c = 66

b + c = 30

Since 'b' and 'c' are both greater than or equal to 18 (otherwise, they would not contribute to the mean of 24), we can say that:

b + c >= 18 + 18 = 36

Therefore, the maximum value of 'a' can be:

a = 66 - 36 = 30

If 'a' is 30, then the data set would be:

18, 18, 30, b, c

The median would be the value of the 3rd observation, which is 30.

Therefore, the answer is option (c) 22.