The frequency distribution of daily working expenditure of families in a locality is as follows:
If the mode of the distribution is $₹ 140$, then the value of $b$ is

• A

  34
• B

  31
• C

  26
• Correct answer
  D

  36

Solution

$$ \text { Frequency distribution is given as } $$
Clearly, modal class is $100-150$, as the maximum frequency occurs in this class. Given, Mode $=140$ We have $$ \text { Mode }=\ell+\frac{f_0-f_{-1}}{2 f_0-f_{-1}-f_1} \times i $$ where $$ \begin{aligned} & \ell=100, f_0=37, f_{-1}=33, f_1=\mathrm{b} \\ & i=50 \end{aligned} $$ Thus, we get $$ 140=100+\left[\frac{37-33}{2(37)-33-b}\right] \times 50 $$ $$ \begin{aligned} & =100+\left[\frac{4}{74-33-b}\right] \times 50 \\ & =100+\frac{200}{41-b} \\ \Rightarrow & 5740=4300+40 b \Rightarrow b=36 \end{aligned} $$

Hence, the correct answer is option: 'D'.