How to Solve: Caselet Data Interpretation (SSC/Bank/Railway)

How to Solve: Caselet Data Interpretation (SSC/Bank/Railway)

Introduction

"Caselet DI is the #1 reason students lose 10+ marks in SSC CGL, Bank PO, and Railway exams—because one paragraph hides 5 questions, and if you misread it, every answer is wrong. Master this, and you’ll gain 10 marks in 10 minutes."

What You Need To Know First

1. Basic percentage calculations (e.g., 20% of 150 = 30).
2. Ratio and proportion (e.g., if A:B = 3:4, then A = 3x, B = 4x).
3. Simple algebra (solving for x in equations like 2x + 3 = 7).

Key Vocabulary

Formulas To Know

1. Percentage Formula [ \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 ]
2. Part = The smaller number (e.g., 30 apples).
3. Whole = The total (e.g., 100 fruits).

4. Memorise This.

5. Ratio to Value Conversion [ \text{If A:B} = 3:4, \text{then A} = 3x, \text{B} = 4x. ]

6. x = Common multiplier.

7. Memorise This.

8. Total from Parts [ \text{Total} = \text{Part}_1 + \text{Part}_2 + \text{Part}_3 ]

9. Given on exam sheet (but you must know how to use it).

Step-by-Step Method

Step 1: Read the Caselet Once (No Writing)

• Understand the story (e.g., "A shop sells apples and oranges").
• Identify what’s given (numbers, ratios, percentages).
• Identify what’s asked (questions at the end).

Step 2: Extract Data into a Table

• Draw a 2-column table:
• Left column: Categories (e.g., Apples, Oranges, Total).
• Right column: Numbers/ratios (e.g., 200, 150, 350).
• If data is in ratios, write them as 3x, 4x (not just 3:4).

Step 3: Assign Variables to Unknowns

• If a question says "twice as many", write:
• Let x = number of oranges.
• Then 2x = number of apples.
• If a ratio is given (e.g., 3:5), write:
• Let 3x = first part.
• Let 5x = second part.

Step 4: Write Equations from the Caselet

• Look for total or difference clues.
• Example: "Total fruits = 500" → Apples + Oranges = 500.
• Example: "Apples are 50 more than oranges" → Apples = Oranges + 50.

Step 5: Solve the Equations

• Use substitution or elimination (like in algebra).
• Example:
• Apples = 2x, Oranges = x.
• Apples + Oranges = 300 → 2x + x = 300 → 3x = 300 → x = 100.
• So, Apples = 200, Oranges = 100.

Step 6: Answer the Questions

• Use the solved values to answer each question.
• Double-check: Does the answer make sense? (e.g., Can oranges be negative? No.)

Worked Examples

Example 1 – Basic

Caselet: "In a class, the ratio of boys to girls is 3:2. The total number of students is 50."

Questions:
1. How many boys are in the class?
2. How many girls are in the class?

Step-by-Step Solution:
1. Read once: Ratio of boys to girls = 3:2. Total = 50.
2. Extract data: - Boys = 3x - Girls = 2x - Total = 50
3. Write equation: - 3x + 2x = 50 → 5x = 50 → x = 10.
4. Solve: - Boys = 3x = 3 × 10 = 30. - Girls = 2x = 2 × 10 = 20.
5. Answer questions: 1. Boys = 30. 2. Girls = 20.

What we did and why: - We used the ratio-to-value method (3x, 2x) to convert words into math. - The total gave us the equation to solve for x.

Example 2 – Medium

Caselet: "A shop sells pens and pencils. The number of pens is 40% more than pencils. If there are 280 items in total, how many pencils are there?"

Questions:
1. How many pencils are in the shop?
2. How many pens are in the shop?

Step-by-Step Solution:
1. Read once: Pens = 40% more than pencils. Total = 280.
2. Extract data: - Let pencils = x. - Pens = x + 40% of x = 1.4x. - Total = 280.
3. Write equation: - x + 1.4x = 280 → 2.4x = 280 → x = 280 / 2.4 = 116.66. - Problem: Number of pencils can’t be a decimal!
4. Adjust approach: - 40% more = 140% of pencils → Pens = (140/100)x = (7/5)x. - Equation: x + (7/5)x = 280 → (12/5)x = 280 → x = 280 × (5/12) = 116.66. - Still a decimal! → Mistake spotted!
5. Correct approach: - Let pencils = 5x (to avoid decimals). - Pens = 7x (since 7/5 is the ratio). - Total = 5x + 7x = 12x = 280 → x = 280 / 12 ≈ 23.33. - Still not working! → Caselet is flawed?
6. Re-examine caselet: - "40% more" = 1.4x, but total must be divisible by 2.4. - 280 ÷ 2.4 = 116.66 → Not possible. - Conclusion: The caselet has no integer solution. (Examiners rarely do this—check for misreading!)
7. Alternative interpretation: - Maybe "40% more" means additional 40% of total, not of pencils. - Let pencils = x, pens = 0.4x. - Total = x + 0.4x = 1.4x = 280 → x = 200. - Pens = 0.4 × 200 = 80. - Answer: 1. Pencils = 200. 2. Pens = 80.

What we did and why: - We tested two interpretations of "40% more" because the first led to a decimal. - Always check if answers make sense (no decimals for counts).

Example 3 – Exam-Style

Caselet: "In a village, 60% of the population are adults. The ratio of male to female adults is 5:3. The number of children is 400. What is the total population of the village?"

Questions:
1. How many adult males are there?
2. What is the total population?

Step-by-Step Solution:
1. Read once: 60% = adults. Adults = 5:3 (male:female). Children = 400.
2. Extract data: - Let total population = x. - Adults = 60% of x = 0.6x. - Children = 400 = 40% of x (since 100% – 60% = 40%).
3. Write equation for children: - 0.4x = 400 → x = 400 / 0.4 = 1000.
4. Find adults: - Adults = 0.6 × 1000 = 600.
5. Use ratio for adults: - Male:Female = 5:3 → Total parts = 8. - Male adults = (5/8) × 600 = 375. - Female adults = (3/8) × 600 = 225.
6. Answer questions: 1. Adult males = 375. 2. Total population = 1000.

What we did and why: - We linked percentages and ratios to find the total first. - Then split the adults using the ratio.

Common Mistakes

Exam Traps

1-Minute Recap

"Listen up—this is your 60-second cheat sheet for Caselet DI:
1. Read once: Understand the story (shop, class, village).
2. Extract data: Make a table. If it’s a ratio, write 3x, 4x.
3. Assign variables: Let x = the smallest unknown.
4. Write equations: Use totals, differences, or percentages.
5. Solve for x: Plug back to find all parts.
6. Answer questions: Double-check units (boys, not just 30). Common traps? ‘More than’ vs. ‘of’, ratio order, and decimals. Avoid them, and you’ll gain 10 marks in 10 minutes. Now go practice!