CAT 2024 Slot 2 — DILR Question 15

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

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

Answer & solution

A
5 : 6
9 : 5
C
5 : 9
D
9 : 4

Solution

Medium

R&D money $=$ PRD% of PAT, i.e. $\text{R\&D}=\text{PRD}\times\text{PAT}$ . PRD is proportional to the bubble's area, and areas are comparable across the two plots. So the R&D ratio is the product of the bubble-area ratio and the PAT ratio for Firm C between the two years.

Firm C readings (areas comparable across both plots):

Year	ES	PAT	Bubble (PRD ∝ area)
2019	600	2400	diameter ≈ 180 (wider)
2023	800	3000	diameter ≈ 120 (smaller)

Write R&D in terms of PRD and PAT. The R&D spend is PRD percent of PAT, so the ratio cancels the constant of proportionality between PRD and bubble area.

\begin{aligned} &\text{R\&D}=\text{PRD}\times\text{PAT}\\ &\Rightarrow\ \dfrac{\text{R\&D}_{2019}}{\text{R\&D}_{2023}}=\dfrac{\text{PRD}_{2019}}{\text{PRD}_{2023}}\times\dfrac{\text{PAT}_{2019}}{\text{PAT}_{2023}} \quad\text{(PRD\;}\propto\text{\;area)} \end{aligned}

Get the PRD (area) ratio from the bubble sizes. Firm C's 2019 bubble is clearly wider than its 2023 bubble; the diameters read as roughly $180$ vs $120$ (a $3:2$ ratio), so the area ratio is the square of that.

\begin{aligned} &\dfrac{\text{PRD}_{2019}}{\text{PRD}_{2023}}=\dfrac{\text{area}_{2019}}{\text{area}_{2023}}=\left(\dfrac{180}{120}\right)^{2} \quad\text{(from chart bubbles)}\\ &\Rightarrow\ =\left(\dfrac{3}{2}\right)^{2}=\dfrac{9}{4}=2.25 \end{aligned}

Combine with the PAT ratio. Substitute the area ratio from step 2 and the PAT values from the Set-up table.

\begin{aligned} &\dfrac{\text{R\&D}_{2019}}{\text{R\&D}_{2023}}=2.25\times\dfrac{2400}{3000} \quad\text{(from step 2)}\\ &\Rightarrow\ =2.25\times 0.8\\ &\Rightarrow\ =1.8=\dfrac{9}{5} \end{aligned}

9:5