If the median of the data x/5, x,x/3, 2x/3,x/4, 2x/5, 3x/5, is 4
Where x > 0 then x = ………………

Correct option is B

Given:

The data is $$\frac{x}{5}, x, \frac{x}{3}, \frac{2x}{3}, \frac{x}{4}, \frac{2x}{5}, \frac{3x}{5}$$​ , and the median is 4 .

Formula Used:

1. The median of a data set is the middle value when the data is arranged in ascending order.
2. If there are n observations:
- For n odd: Median is the $$\frac{n+1}{2}$$​th value in the ordered set.

Solution:

1. Number of Observations:
The given data has n = 7 observations.

2. Arrange in Ascending Order:
Sorting the data:

$$\frac{x}{5}, \frac{x}{4}, \frac{x}{3}, \frac{2x}{5}, \frac{3x}{5}, \frac{2x}{3}, x$$​​

3. Find the Median:
Since n = 7 (odd), the median is the $$\frac{7+1}{2} = 4 th$$​ value in the ordered data.
The 4th value is $$\frac{2x}{5}$$​ .

4. Given Condition:
The median is 4 , so:

$$\frac{2x}{5} = 4$$​​

5. Solve for x :
Multiply both sides by 5 :

2x = 20

Divide by 2 :

x = 10

Final Answer:

Option B: 10