The frequency distribution of daily working expenditure of families in a locality is as follows:

If the mode of the distribution is Rs. 140, then the value of $$b$$ is

The class-interval that contains the modal value Rs. 140 is the interval $$140\!-\!160$$. Hence this is the modal class.

Let
  $$l = 140$$ be the lower boundary of the modal class,
  $$h = 20$$ be the class width,
  $$f_1 = b$$ be the frequency of the modal class,
  $$f_0 = 36$$ be the frequency of the class just before the modal class, and
  $$f_2 = 31$$ be the frequency of the class just after the modal class.

The empirical formula for the mode of a grouped frequency distribution is
$$ \text{Mode} = l + \frac{f_1 - f_0}{2f_1 - f_0 - f_2}\;h $$

Substituting the numerical values and the given mode (Rs. 140), we get
$$ 140 = 140 + \frac{b - 36}{2b - 36 - 31}\;(20) $$

Since the two 140’s on either side are the same, the additive term on the right must be zero. That happens only when the numerator vanishes, i.e.
$$ b - 36 = 0 \quad\Longrightarrow\quad b = 36. $$

Thus the missing frequency is $$b = 36$$.

Option D which is: 36