CAT 2024 Slot 2 — DILR Question 14

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

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?

Answer & solution

A
Firm A
B
Firm B
C
Firm C
Firm E

Solution

Medium

If the annual rate of growth (ARG) of PAT is constant, then PAT grows by the same factor every year. Over the fixed gap from 2019 to 2023 the firm whose PAT multiplies by the largest factor must have the highest ARG — so we just compare the ratio $\dfrac{\text{PAT}_{2023}}{\text{PAT}_{2019}}$ for each firm.

Readings from the two plots (ES on horizontal axis, PAT on vertical axis; bubble size ∝ PRD):

Firm	ES 2019	PAT 2019	PRD 2019	ES 2023	PAT 2023	PRD 2023
A	800	3000	medium	1300	3900	medium
B	1000	2800	med-large	1000	3800	large
C	600	2400	medium	800	3000	medium
D	600	3900	small	800	2400	small
E	1200	2500	large	1400	3500	large
F	800	2500	small	1000	3200	small

Constant ARG means equal-factor growth. If ARG $=r$ each year, then $\text{PAT}_{2023}=\text{PAT}_{2019}\,(1+r)^{4}$ . The number of years (4) is the same for every firm, so a larger growth factor $\dfrac{\text{PAT}_{2023}}{\text{PAT}_{2019}}$ means a larger $r$ .

\begin{aligned} &\text{PAT}_{2023}=\text{PAT}_{2019}\,(1+r)^{4}\\ &\Rightarrow\ (1+r)^{4}=\dfrac{\text{PAT}_{2023}}{\text{PAT}_{2019}} \quad\text{(same 4-year gap for all)}\\ &\Rightarrow\ \text{rank ARG by the ratio }\dfrac{\text{PAT}_{2023}}{\text{PAT}_{2019}} \end{aligned}

Compute the PAT growth factor for each candidate. Read PAT for 2019 and 2023 from the Set-up table.

\begin{aligned} &A:\ \dfrac{3900}{3000}=1.30 \quad\text{(from chart)}\\ &\Rightarrow\ B:\ \dfrac{3800}{2800}\approx 1.36\\ &\Rightarrow\ C:\ \dfrac{3000}{2400}=1.25\\ &\Rightarrow\ E:\ \dfrac{3500}{2500}=1.40 \end{aligned}

Pick the largest factor. Among A, B, C and E the largest growth factor is Firm E's $1.40$ , so E had the highest ARG.

\begin{aligned} &1.40\;(E)\;>\;1.36\;(B)\;>\;1.30\;(A)\;>\;1.25\;(C) \end{aligned}

\text{Firm E}