CAT 2024 Slot 2 · DILR · Set 5: PAT, Employee Strength and R&D of Six Firms

The full set and all 4 questions (Q19–Q22) from CAT 2024 Slot 2, with answers and solutions.

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.

Question 19 · Mixed DI (Radar, Triangular, Stock etc)

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. A

    Firm E

  2. B

    Firm B

  3. C

    Firm C

  4. D

    Firm A

Pick an option, then check.
Answer & solution

Answer: Option A

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

If PAT grows at a constant rate r every year, PAT 2023 = PAT 2019 × (1 + r)⁴. So the firm with the largest ratio PAT 2023/PAT 2019 has the highest ARG.

Firm

PAT 2019

PAT 2023

PAT 2023 / PAT 2019

A

3000

3900

1.30

B

2800

3800

1.36

C

2400

3000

1.25

E

2400

3500

1.46

Firm E has the highest ratio.

Hence, the answer is option 1.

Question 20 · Mixed and Combination Charts

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

  1. A

    9 : 4

  2. B

    5 : 9

  3. C

    9 : 5

  4. D

    5 : 6

Pick an option, then check.
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.

Question 21 · Mixed DI (Radar, Triangular, Stock etc)

Which among the firms A, C, E, and F had the maximum PAT per employee in 2023?

  1. A

    Firm C

  2. B

    Firm F

  3. C

    Firm A

  4. D

    Firm E

Pick an option, then check.
Answer & solution

Answer: Option A

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

Firm

PAT 2023 (Rs cr)

ES 2023

PAT per employee

A

3900

1300

3.00

C

3000

800

3.75

E

3500

1400

2.50

F

3200

1000

3.20

Firm C has the maximum PAT per employee.

Hence, the answer is option 1.

Question 22 · Mixed DI (Radar, Triangular, Stock etc)

Which among the firms C, D, E, and F had the least amount of R&D spending per employee in 2023?

  1. A

    Firm C

  2. B

    Firm D

  3. C

    Firm F

  4. D

    Firm E

Pick an option, then check.
Answer & solution

Answer: Option B

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

Firm

PAT 2023

PRD units

R&D (∝ PAT × PRD)

ES 2023

R&D per employee

C

3000

4

12000

800

15.0

D

2400

4

9600

800

12.0

E

3500

9

31500

1400

22.5

F

3200

4

12800

1000

12.8

Firm D has the least R&D spending per employee. Note that C, D and F have equal circles in 2023, so among them the smallest PAT/ES wins (D: 3.0 against C: 3.75 and F: 3.2); E has a much bigger circle.

Hence, the answer is option 2.

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