Comprehension:

The two plots below give the following information about six firms A, B, C, D, E, and F for 2019 and 2023. PAT: The firm’s profits after taxes in Rs. crores, ES: The firm’s employee strength, that is the number of employees in the firm, and PRD: The percentage of the firm’s PAT that they spend on Research and Development (RandD). In the plots, the horizontal and vertical coordinates of point representing each firm gives their ES and PAT values respectively. The PRD values of each firm are proportional to the areas around the points representing each firm. The areas are comparable between the two plots, i.e., equal areas in the two plots represent the same PRD values for the two years.

Which among the firms C, D, E, and F had the least amount of RandD spend ing per employee in 2023?

Correct Answer: Option D (Firm D)

To find the firm with the least amount of R&D spending per employee in 2023, let's break down the information given in the plots:
1. Employee Strength (ES): Represented by the horizontal coordinate (X-axis) of the point.
2. Profit After Taxes (PAT): Represented by the vertical coordinate (Y-axis) of the point.
3. Percentage of PAT spent on R&D (PRD): Proportional to the area of the circle around each point. Since the area of a circle is proportional to the square of its size, we can denote the area (and thus the PRD value) of the standard small circle as $A$.

The total R&D spending of a firm is calculated as:
$\text{R\&D Spending}=\text{PAT}\times \text{PRD}$
Therefore, the R&D spending per employee is:
$\text{R\&D Spending per Employee}=\frac{\text{PAT}\times \text{PRD}}{\text{ES}}$

Now, let's read the values from the 2023 plot for the relevant firms (C, D, E, and F):
- Firm D: Located at $\text{ES}=800$ and $\text{PAT}=2400$. The circle is small, representing area $A$.
- Firm E (labeled as "G" in the 2023 plot): Located at $\text{ES}=800$ and $\text{PAT}=3000$. The circle has the same small size, representing area $A$.
- Firm F: Located at $\text{ES}=1000$ and $\text{PAT}=3200$. The circle also has the same small size, representing area $A$.
- Firm C: Located at $\text{ES}=1400$ and $\text{PAT}=3500$. The circle is significantly larger, with an area estimated to be at least $3A$.

Next, we calculate the relative R&D spending per employee (expressed in terms of $A$) for each firm:
- For Firm D:
$\frac{2400\times A}{800}=3A$
- For Firm E:
$\frac{3000\times A}{800}=3.75A$
- For Firm F:
$\frac{3200\times A}{1000}=3.2A$
- For Firm C:
$\frac{3500\times (\text{Area}>3A)}{1400}=2.5\times \text{Area}>7.5A$

Comparing the calculated values:
$3A<3.2A<3.75A<7.5A$
Thus, Firm D has the least amount of R&D spending per employee in 2023.