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 (R&D).

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.

Q. 1 Assume that the annual rate of growth in PAT over the previous year (ARG) remained constant over the years for each of the six firms. Which among the firms A, B, C, and E had the highest ARG?
1) Firm B 2) Firm C 3) Firm A 4) Firm E
Q. 2 The ratio of the amount of money spent by Firm C on R&D in 2019 to that in 2023 is closest to
1) 9 : 4 2) 5 : 9 3) 9 : 5 4) 5 : 6
Q. 3 Which among the firms A, C, E, and F had the maximum PAT per employee in 2023?
1) Firm A 2) Firm F 3) Firm E 4) Firm C
Q. 4 Which among the firms C, D, E, and F had the least amount of R&D spending per employee in 2023?
1) Firm D 2) Firm C 3) Firm E 4) Firm F

Firm Analysis: PAT, ES and R&D (2019 vs 2023)

Q1. Highest Annual Rate of Growth (ARG) in PAT

We use the formula for annual compound growth:

\[ \text{ARG} = \left( \frac{\text{PAT}_{2023}}{\text{PAT}_{2019}} \right)^{\frac{1}{4}} – 1 \]

Estimate values:

• Firm A: \( \frac{4000}{2900} \approx 1.38 \)
• Firm B: \( \frac{3900}{2700} \approx 1.44 \)
• Firm C: \( \frac{3100}{2500} \approx 1.24 \)
• Firm E: \( \frac{3500}{2400} \approx 1.46 \)

Answer: Firm E (Option 4)

Q2. Ratio of R&D Spending of Firm C (2019 to 2023)

We estimate R&D amount as:

\[ \text{R\&D} = \text{PAT} \times \text{PRD} \]

Since area of bubble \( \propto \text{PRD} \propto r^2 \):

\[ \text{Ratio} = \frac{2500 \times 9}{3100 \times 4} \approx \frac{22500}{12400} \approx \frac{9}{5} \]

Answer: 9:5 (Option 3)

Q3. Maximum PAT per Employee in 2023

We calculate:

\[ \text{PAT per employee} = \frac{\text{PAT}}{\text{ES}} \]

• Firm A: \( \frac{4000}{1300} \approx 3.08 \)
• Firm C: \( \frac{3100}{800} \approx 3.88 \)
• Firm E: \( \frac{3500}{1400} \approx 2.50 \)
• Firm F: \( \frac{3300}{1000} \approx 3.30 \)

Answer: Firm C (Option 4)

Q4. Least R&D per Employee in 2023

We calculate R&D per employee as:

\[ \frac{\text{R\&D Spending}}{\text{ES}} = \frac{\text{PAT} \times \text{PRD}}{\text{ES}} \propto \frac{\text{Bubble Area}}{\text{ES}} \]

By visual estimation:

• Firm D has smallest bubble and relatively small ES (~750)
• Others (C, E, F) have larger bubbles or ES

Answer: Firm D (Option 1)