CAT 2024 Slot 2 — DILR Question 17

Bubble ChartsEasy

Passage / Data

Answer the following questions based on the information given below.

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 the point representing each firm give 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.

Firms plot 2019

Firms plot 2023

Approximate 2019 readings (ES on the horizontal axis, PAT on the vertical axis; bubble size ∝ PRD):

Firm (2019)	ES (approx.)	PAT (approx.)	Bubble size (PRD)
A	800	3000	medium
B	1000	2800	medium-large
C	600	2400	medium
D	600	3900	small
E	1200	2500	large
F	800	2500	small

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

Answer & solution

Firm D
B
Firm F
C
Firm E
D
Firm C

Solution

Medium

R&D spend $=\text{PRD}\times\text{PAT}$ and PRD $\propto$ bubble area, so R&D per employee $=\dfrac{\text{PRD}\times\text{PAT}}{\text{ES}}$ . Use the 2023 bubble sizes for PRD and the 2023 PAT and ES coordinates.

2023 readings (bubble size $\propto$ PRD):

Firm	ES 2023	PAT 2023	PRD (bubble)
C	800	3000	medium
D	800	2400	small
E	1400	3500	large
F	1000	3200	small

Express R&D per employee. Since R&D $=\text{PRD}\times\text{PAT}$ , the per-employee figure is that product divided by ES.

\begin{aligned} &\text{R\&D per employee}=\dfrac{\text{PRD}\times\text{PAT}}{\text{ES}} \quad\text{(PRD}\propto\text{bubble area)} \end{aligned}

Compare the two small-bubble firms first. C has a medium bubble and E a large bubble, so both carry a higher PRD than the small-bubble firms D and F; the minimum must be D or F. With equal (small) PRD, compare $\dfrac{\text{PAT}}{\text{ES}}$ .

\begin{aligned} &D:\ \dfrac{\text{PAT}}{\text{ES}}=\dfrac{2400}{800}=3.0 \quad\text{(small bubble)}\\ &\Rightarrow\ F:\ \dfrac{\text{PAT}}{\text{ES}}=\dfrac{3200}{1000}=3.2 \quad\text{(small bubble)} \end{aligned}

Conclude. D and F share the smallest PRD, but D has the lower $\text{PAT}/\text{ES}$ (and the smaller bubble of the two), so D's R&D per employee is the least. C (medium PRD) and E (large PRD) are clearly higher.

\begin{aligned} &\text{R\&D/emp: } D\;<\;F\;<\;C,\,E \quad\text{[(small,3.0)} < \text{(small,3.2)]} \end{aligned}

\text{Firm D}