Consider the data 

The difference of the upper limit of the median class and the lower limit of the modal class is:

To find median and mode of given grouped data we need to find cumulative
frequency (N). Cumulative frequency table is:

The class whose cumulative frequency is greater than or near to ( The term is called a 𝑁
2
)
𝑡ℎ
median class of grouped data.

$\begin{array}{r}{\left(\frac{N}{2}\right)}^{\text{th }}\text{ term }={\left(\frac{67}{2}\right)}^{\text{th }}\text{ term }\\ =(33.5{)}^{\text{th }}\text{ term }\end{array}$

It lies in 125 − 145 class.

Hence the upper limit of median class is 145.
Modal class refers to the class having the highest frequency. The highest frequency is 20 and
20 lies in 125 − 145 class.
The lower limit of modal class is 125.
The required difference = upper limit of median class − lower limit of modal class
= 145 − 125
= 20
Therefore, the difference between the upper limit of median class and lower limit of modal
class is 20.
Hence, option (c) 20 is correct.