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.

The ratio of the amount of money spent by Firm C on R and D in 2019 to that in 2023 is closest to:

The correct option is 9 : 5.

To find the ratio of the amount of money spent by Firm C on R&D in 2019 to that in 2023, we can break down the problem as follows:

1. Formula for Money Spent on R&D:
The amount of money spent on R&D is given by:
$$\text{R\&D Spend}=\text{PAT}\times \text{PRD}$$
where:
- PAT (Profit After Taxes) is represented by the vertical coordinate (y-axis coordinate) of each firm's center point.
- PRD is the percentage of PAT spent on R&D, which is proportional to the area of the circle representing the firm.

2. Analyze Firm C in 2019:
- Looking at the 2019 plot, the center of the bubble representing Firm C is located at:
- Horizontal coordinate (ES) = 600 - Vertical coordinate (PAT) = 2400 Rs. crores
So, ${\text{PAT}}_{2019}=2400$.
- The bubble for Firm C in 2019 spans vertically from approximately 2100 to 2700 on the y-axis. This corresponds to a diameter ($D_{2019}$) of:
$D_{2019}=2700-2100=600\text{units}$
- Since the area of a circle is proportional to the square of its diameter ($\text{Area}\propto D^2$):
${\text{PRD}}_{2019}\propto {600}^2=\mathrm{360,000}$

3. Analyze Firm C in 2023:
- Looking at the 2023 plot, the center of the bubble representing Firm C is located at:
- Horizontal coordinate (ES) = 1400 - Vertical coordinate (PAT) = 3500 Rs. crores (midpoint between 3400 and 3600)
So, ${\text{PAT}}_{2023}=3500$.
- The bubble for Firm C in 2023 spans vertically from approximately 3300 to 3700 on the y-axis. This corresponds to a diameter ($D_{2023}$) of:
$D_{2023}=3700-3300=400\text{units}$
- Thus, the PRD of Firm C in 2023 is proportional to:
${\text{PRD}}_{2023}\propto {400}^2=\mathrm{160,000}$

4. Calculate the Ratio of R&D Spend:
The ratio of money spent by Firm C in 2019 to that in 2023 is:
$$\frac{{\text{R\&D Spend}}_{2019}}{{\text{R\&D Spend}}_{2023}}=\frac{{\text{PAT}}_{2019}\times {\text{PRD}}_{2019}}{{\text{PAT}}_{2023}\times {\text{PRD}}_{2023}}$$
Substituting the estimated values:
$$\frac{{\text{R\&D Spend}}_{2019}}{{\text{R\&D Spend}}_{2023}}=\frac{2400}{3500}\times \frac{\mathrm{360,000}}{\mathrm{160,000}}$$
$$\frac{{\text{R\&D Spend}}_{2019}}{{\text{R\&D Spend}}_{2023}}=\frac{24}{35}\times \frac{9}{4}=\frac{6}{35}\times 9=\frac{54}{35}\approx 1.54$$

5. Comparing with the Given Options:
- 9 : 4 = 2.25
- 9 : 5 = 1.80
- 5 : 6 ≈ 0.83
- 5 : 9 ≈ 0.56
The calculated ratio of approximately 1.54 is closest to 9 : 5 (1.80).