CAT 2024 Slot 2 · DILR · Question 20
CAT 2024 Slot 2 previous year question on Mixed and Combination Charts, with the answer and a step-by-step solution.
Set 5: PAT, Employee Strength and R&D of Six Firms — this question belongs to a set. Read the full set with all 4 questions →
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.
The ratio of the amount of money spent by Firm C on R&D in 2019 to that in 2023 is closest to
- A
9 : 4
- B
5 : 9
- C
9 : 5
- D
5 : 6
Answer & solution
Answer: Option C
Solving the set
Step 1 – Read each firm's ES (horizontal axis) and PAT (vertical axis) from the two plots.
Step 2 – Read the circle sizes. Taking the smallest circle (D in 2019) as radius 1 unit, the other circles have radii of 2, 3 or 4 units. PRD is proportional to the area, i.e., to radius², so the PRD 'units' are 1, 4, 9 and 16.
|
Firm |
ES 2019 |
PAT 2019 |
Radius 2019 |
PRD 2019 (units) |
ES 2023 |
PAT 2023 |
Radius 2023 |
PRD 2023 (units) |
|
A |
800 |
3000 |
2 |
4 |
1300 |
3900 |
2 |
4 |
|
B |
1000 |
2800 |
3 |
9 |
1000 |
3800 |
3 |
9 |
|
C |
600 |
2400 |
3 |
9 |
800 |
3000 |
2 |
4 |
|
D |
600 |
3900 |
1 |
1 |
800 |
2400 |
2 |
4 |
|
E |
1200 |
2400 |
4 |
16 |
1400 |
3500 |
3 |
9 |
|
F |
800 |
2500 |
2 |
4 |
1000 |
3200 |
2 |
4 |
Step 3 – Useful formulas. R&D spending = PAT × PRD/100, so R&D is proportional to PAT × (PRD units). PAT per employee = PAT/ES.
This question
From the table, Firm C's circle has radius 3 in 2019 and 2 in 2023, so its PRD units are 9 and 4.
R&D 2019 : R&D 2023 = (2400 × 9) : (3000 × 4) = 21600 : 12000 = 9 : 5.
Hence, the answer is option 3.
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