If the mode of the following data is 140, then what is the value of x?

Class	125-130	130-135	135-140	140-145	145-150
Frequency	30	30	33	x	31

Correct option is B

Given:

Classes (width (h=5)): 125–130, 130–135, 135–140, 140–145, 145–150
Frequencies: 30, 30, 33, x, 31
Mode = 140

modal class is (140 -145).
For modal class: preceding freq $$f_0=33$$​, modal freq $$f_1$$​ = x, succeeding freq $$f_2=$$​31, lower limit l = 140.

Formula Used:
Mode (grouped data):
​$$\text{Mode}=l+\frac{(f_1-f_0)}{2f_1-f_0-f_2}\cdot h$$​​

Solution:
Given Mode=140 and l = 140:
140=1$$40+\frac{(x-33)}{2x-33-31}\times 5$$​​
​$$\frac{(x-33)}{2x-64}\times 5=0$$​​
x-33=0
x = 33