In-Depth: Ratio and Proportion

CLAT Application & Relevance

Importance: VERY HIGH. Along with percentages and averages, Ratios and Proportions form the backbone of Data Interpretation. They are used extensively to compare quantities, distribute totals, and understand relationships between different data points within a passage, table, or graph.

How it's tested: Finding ratios of different categories from a bar graph or table; dividing a total quantity (e.g., budget, population) into parts based on a given ratio; combining ratios from multiple sources to find a new relationship; direct/inverse variation problems hidden in caselets.

Section 1: Core Concepts & Techniques

A Ratio is a comparison of two or more quantities of the same kind by division. A Proportion is an equality of two ratios.

Key Concepts & Techniques

Ratio Notation: A ratio of 'a' to 'b' is written as a:b or a/b.
Simplifying Ratios: Always express a ratio in its simplest form by dividing both parts by their Highest Common Factor (HCF). E.g., 150:200 simplifies to 3:4.
Dividing a Quantity in a Given Ratio: If a total quantity 'T' is to be divided among parts in the ratio a:b, then:
- First part = (a / (a+b)) * T
- Second part = (b / (a+b)) * T
This extends for more than two parts (e.g., a:b:c).
Combining Ratios: When a common term exists between two ratios (e.g., A:B and B:C), make the common term's value equal in both ratios by finding its LCM.
Example: If A:B = 2:3 and B:C = 4:5. LCM of 3 and 4 (common term B) is 12.
A:B = (2*4):(3*4) = 8:12
B:C = (4*3):(5*3) = 12:15
Combined Ratio A:B:C = 8:12:15.
Direct Variation: If two quantities X and Y are directly proportional, X = kY (or X1/Y1 = X2/Y2). As X increases, Y increases.
Inverse Variation: If two quantities X and Y are inversely proportional, X = k/Y (or X1Y1 = X2Y2). As X increases, Y decreases.

Section 2: Solved CLAT-Style Examples

Example 1: Dividing a Total Quantity based on Ratio (Caselet)

Passage Context: A law firm earned a profit of ₹9,00,000 from a major case. This profit is to be distributed among the senior partner, junior partner, and associates in the ratio of their efforts, which is 5:3:2 respectively.

Question: "How much money will the junior partner receive?"

Detailed Solution:
1. Identify Total Quantity and Ratio: Total Profit (T) = ₹9,00,000 Ratio (Senior : Junior : Associates) = 5 : 3 : 2
2. Calculate Total Ratio Parts: 5 + 3 + 2 = 10 parts.
3. Determine Junior Partner's Share: The junior partner's share is 3 parts out of 10.
Junior Partner's Share = (3 / 10) * 9,00,000
= 3 * 90,000 = ₹2,70,000.
Answer: The junior partner will receive ₹2,70,000.

Example 2: Combining Ratios from Different Data Points (Table/Caselet)

Passage Context: A university's student body across three departments - Law, Humanities, and Commerce - is detailed. The ratio of Law students to Humanities students is 4:3. The ratio of Humanities students to Commerce students is 2:5.

Question: "What is the combined ratio of Law : Humanities : Commerce students?"

Detailed Solution:
1. List Given Ratios: Law : Humanities (L:H) = 4 : 3 Humanities : Commerce (H:C) = 2 : 5
2. Identify Common Term: The common term is 'Humanities'. Its values are 3 and 2.
3. Find LCM of Common Term Values: LCM of 3 and 2 is 6.
4. Adjust Ratios to Make Common Term Equal to LCM: For L:H = 4:3, multiply both by 2 to make Humanities 6: L:H = (4*2) : (3*2) = 8 : 6 For H:C = 2:5, multiply both by 3 to make Humanities 6: H:C = (2*3) : (5*3) = 6 : 15
5. Combine the Ratios: Now that 'Humanities' is 6 in both, we can combine.
L : H : C = 8 : 6 : 15.
Answer: The combined ratio of Law : Humanities : Commerce students is 8:6:15.