In-Depth: Mixed Graphs

CLAT Application & Relevance

Importance: VERY HIGH. Mixed graphs (or compound graphs) are a staple in the modern CLAT. They combine two or more different types of data visualization (e.g., a bar graph with a pie chart, or a table with a line graph) to present a more comprehensive data set. This format tests your ability to synthesize information from various sources, identifying correlations and applying arithmetic across different visual representations.

How it's tested: Questions require extracting data from one graph and using it in conjunction with data from another; calculating percentages, ratios, or averages by combining information from both graphs; identifying trends and distributions simultaneously; problems often span multiple steps, requiring careful planning.

Section 1: Core Concepts & Strategic Approach

Mixed graphs present related data using a combination of charts and/or tables. The key challenge is to understand how the different components of the data visualization relate to each other.

Common Combinations:

Pie Chart & Table/Bar Graph: A pie chart showing overall distribution (e.g., expenses by category), with a table or bar graph providing details for specific categories or sub-categories over time.
Line Graph & Bar Graph: A line graph showing trends (e.g., revenue over years), and a bar graph showing discrete values (e.g., number of employees per year) or a breakdown of revenue components for each year.
Two Tables: Information spread across two related tables that need to be cross-referenced.

Strategic Approach to Mixed Graphs:

Understand Each Graph Individually: Before looking at questions, quickly understand what each graph/table represents, its axes, units, and what kind of information it conveys. Identify if one graph's total or component is a part of another graph.
Identify Relationships: Crucially, figure out how the graphs are connected. Does one graph show percentages of a total, while another shows the total itself or details of one of those percentages? A common link is a 'total' or a specific category.
Read Questions Carefully: Each question will guide you on which graph(s) to refer to and which operations to perform.
Extract & Synthesize: Extract data from the necessary graph(s). If data from multiple graphs is needed, often converting percentages/ratios to absolute values (or vice-versa) is the first step.
Step-by-Step Calculation: Break down complex problems into smaller, manageable steps.

Section 2: Solved CLAT-Style Examples

Example 1: Pie Chart & Table Combination

Passage Context: A law school has a total of 1500 students in 2023. Pie Chart 1 shows the percentage distribution of students across three programs: LLB, LLM, and PhD. Table 1 provides the ratio of male to female students within each program.

Pie Chart 1: Program-wise Student Distribution (Total: 1500)

Placeholder Pie Chart showing: LLB: 60%, LLM: 25%, PhD: 15%

(Data: LLB: 60%, LLM: 25%, PhD: 15%)

Table 1: Male to Female Ratio in Each Program

Program	Male : Female Ratio
LLB	3 : 2
LLM	2 : 3
PhD	1 : 1

Question A: "What is the total number of female students in the law school?"

Detailed Solution A:
1. Calculate Total Students in each Program (from Pie Chart 1):
LLB Students = 60% of 1500 = 0.60 * 1500 = 900
LLM Students = 25% of 1500 = 0.25 * 1500 = 375
PhD Students = 15% of 1500 = 0.15 * 1500 = 225
(Check: 900 + 375 + 225 = 1500. Correct.)
2. Calculate Female Students in each Program (from Table 1 and calculated totals):
LLB: Total 900. Male:Female = 3:2. Total parts = 5.
Female LLB = (2 / 5) * 900 = 360
LLM: Total 375. Male:Female = 2:3. Total parts = 5.
Female LLM = (3 / 5) * 375 = 225
PhD: Total 225. Male:Female = 1:1. Total parts = 2.
Female PhD = (1 / 2) * 225 = 112.5 (Real-world note: Student numbers must be whole. CLAT often uses numbers that simplify. For simplicity, we'll proceed, but in CLAT, numbers are usually chosen to avoid fractions). Let's adjust PhD total to 200 for clean numbers, if it were an actual exam: PhD is 15% of 1500=225, so for simplicity in this example let's assume total is 1400 so PhD is 210, if it were 1400 then 15% of 1400 = 210. So Female PhD = 105. For now, we stick to the calculated 225, and fractional female count for the exercise.
3. Calculate Total Female Students:
Total Female = Female LLB + Female LLM + Female PhD = 360 + 225 + 112.5 = 697.5.
Answer A: The total number of female students in the law school is 697.5 (approx 698 if rounded up).

Example 2: Bar Graph & Line Graph Combination (Sales & Growth)

Passage Context: Bar Graph 1 shows the total sales (in Lakhs ₹) of a legal tech company 'LawServe' for four products (A, B, C, D) in 2022. Line Graph 1 shows the percentage growth of sales for each product from 2022 to 2023.

Bar Graph 1: LawServe Product Sales (2022, in ₹ Lakhs)

Placeholder Bar Graph showing sales: Product A: 120, B: 150, C: 100, D: 80

(Data: Product A: 120, B: 150, C: 100, D: 80)

Line Graph 1: Percentage Growth 2022 to 2023

Placeholder Line Graph showing growth: Product A: 25%, B: 20%, C: 30%, D: 15%

(Data: Product A: 25%, B: 20%, C: 30%, D: 15%)

Question: "What was the total sales revenue of LawServe for all products combined in 2023?"

Detailed Solution:
1. Calculate 2023 Sales for each Product: 2023 Sales = 2022 Sales * (1 + Growth%/100)
Product A: 2022 Sales = 120. Growth = 25%.
2023 Sales A = 120 * (1 + 25/100) = 120 * 1.25 = 150 Lakhs.
Product B: 2022 Sales = 150. Growth = 20%.
2023 Sales B = 150 * (1 + 20/100) = 150 * 1.20 = 180 Lakhs.
Product C: 2022 Sales = 100. Growth = 30%.
2023 Sales C = 100 * (1 + 30/100) = 100 * 1.30 = 130 Lakhs.
Product D: 2022 Sales = 80. Growth = 15%.
2023 Sales D = 80 * (1 + 15/100) = 80 * 1.15 = 92 Lakhs.
2. Calculate Total Sales for 2023:
Total 2023 Sales = 150 + 180 + 130 + 92 = 552 Lakhs.
Answer: The total sales revenue for LawServe in 2023 was ₹552 Lakhs.