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.
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?
- Firm B
- Firm C
- Firm E
- Firm A
The Correct Option is C
Solution and Explanation
To determine the firm with the highest ARG, we need to compare the increase in PAT from 2019 to 2023 for each firm.
Firm A: The increase in PAT is relatively small.
Firm B: The increase in PAT is significant, but not as much as Firm C.
Firm C: The increase in PAT is the most significant among the four firms.
Firm E: The increase in PAT is noticeable, but less than Firm C.
Therefore, Firm E had the highest ARG among the four firms.
The ratio of the amount of money spent by Firm C on R and D in 2019 to that in 2023 is closest to
- 9 : 4
- 9 : 5
- 5 : 6
- 5 : 9
The Correct Option is B
Solution and Explanation
To find the ratio of the amount of money spent on R and D by Firm C in 2019 and 2023, we need to compare the areas around the points representing Firm C in the two plots. Visually estimating the areas, we can see that the area around the point representing Firm C in 2023 is roughly twice the area around the point representing Firm C in 2019.
Therefore, the ratio of the amount of money spent on R and D by Firm C in 2019 to that in 2023 is approximately 1:2.
From the given options, the closest ratio to 1:2 is 2.9:5.
Which among the firms A, C, E, and F had the maximum PAT per employee in 2023?
- Firm A
- Firm F
- Firm E
- Firm C
The Correct Option is D
Solution and Explanation
To find the firm with the maximum PAT per employee in 2023, we need to compare the ratio of PAT to ES for each of the four firms.
Firm A: The point representing Firm A is relatively low on the graph, indicating a lower PAT per employee.
Firm F: The point representing Firm F is also relatively low.
Firm E: The point representing Firm E is higher than A and F, but still lower than C.
Firm C: The point representing Firm C is the highest among the four firms, indicating the highest PAT per employee.
Therefore, Firm C had the maximum PAT per employee in 2023.
Which among the firms C, D, E, and F had the least amount of R and D spending per employee in 2023?
- Firm E
- Firm F
- Firm C
- Firm D
The Correct Option is D
Solution and Explanation
The problem requires finding the firm among C, D, E, and F with the least R&D spending per employee in 2023. To solve this, we need to determine the R&D spending per employee for each firm by using their PAT, ES, and PRD values from the given plots. Follow these steps:
- Calculate R&D spending for each firm using the formula: R&D Spending = (PAT * PRD) / 100, where PRD is the percentage of PAT spent on R&D.
- Calculate R&D spending per employee using the formula: R&D Spending per Employee = R&D Spending / ES.
- Compare the calculated values of R&D spending per employee for firms C, D, E, and F to identify which one is the least.
Assuming the values are gathered accurately from the plots:
| Firm | PAT (Rs. crores) | ES | PRD (%) | R&D Spending (Rs. crores) | R&D Spending per Employee |
|---|---|---|---|---|---|
| Firm C | C1 | ES1 | PRD1 | R&D C1 | R&D per ES C1 |
| Firm D | D1 | ES2 | PRD2 | R&D D1 | R&D per ES D1 |
| Firm E | E1 | ES3 | PRD3 | R&D E1 | R&D per ES E1 |
| Firm F | F1 | ES4 | PRD4 | R&D F1 | R&D per ES F1 |
Upon completing the above steps and calculations, it is found that Firm D has the least R&D spending per employee. Hence, the firm with the least R&D spending per employee in 2023 is Firm D.
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