Caselet and Advanced Calculation DI

Of all SBI PO Data Interpretation formats, the caselet is the one that breaks more aspirants than any chart or table. There is no diagram. There is no pre-built grid. Just a paragraph — sometimes a single dense one — that you must convert into structured numbers, often under 90 seconds of clock pressure. This lesson is about that conversion process.

Definition: A caselet DI is a data interpretation set in which information is presented as continuous prose, with numbers buried inside sentences rather than displayed as a chart or table. The aspirant must read, extract, and re-organise the data before any calculation begins.

Definition: A linking word is a verbal cue ("remaining", "twice", "one-third more than", "half of", "rest", "out of which") that signals an arithmetic or logical relationship between two quantities.

Why caselets feel harder than they are

The difficulty of a caselet is mostly organisational, not mathematical. The numbers themselves are usually simple — additions, percentages, ratios, a two-variable equation, or a Venn diagram. What kills time is re-reading the paragraph because you tried to "hold it in your head." If you spend the first 60–90 seconds tabulating, the calculations that follow are easy.

The official rule of thumb in PO coaching is brutal but correct: never attempt a caselet in your head. Underline, then table.

A four-step strategy that works in 90 seconds

1. Read once, fully, without writing. Get a feel for what is being described — is it a budget split? People in a city? Sales across days?
2. Underline every number and its label. "120 students", "20% boys", "remaining girls" — circle each pairing.
3. Build your own scaffolding. A two-column table for two-variable problems, a 3×3 grid for three-category breakdowns, or a Venn diagram for set-based caselets.
4. Watch for the linking words and translate them into equations.

Why it matters: SBI PO Mains DI has 30 marks in 45 minutes. A well-executed caselet pays the best return per minute in the entire paper, because most candidates skip them. Two solved caselets can lift a borderline score into the call-list zone.

Translating linking words into algebra

Once the data is on paper, the language becomes equations. A short reference:

• "A is 20 more than B" → A = B + 20
• "A is twice B" → A = 2B
• "Half of A is equal to B" → A/2 = B, i.e., A = 2B
• "One-third more than B" → A = B + B/3 = 4B/3
• "Remaining" or "Rest" → (Total) − (what is already assigned)
• "Out of which" → a subset relation

Worked example for the classic two-equation case:

Question: A and B together have Rs 180. A is 20 more than B. Find A and B.

Solution:
Step 1: Let B = x. Then A = x + 20 (translating "A is 20 more than B").
Step 2: A + B = 180, so (x + 20) + x = 180 → 2x = 160 → x = 80.
Step 3: B = 80, and A = 100.
Conclusion: A has Rs 100, B has Rs 80.

That is a six-line algebra problem hidden inside a paragraph. The skill is spotting it, not solving it.

Set-based caselets — the Venn diagram trick

When the paragraph mentions categories like "people who like tea / coffee / both / neither," draw a two-set Venn the moment you start reading. Use these formulas:

• n(A ∪ B) = n(A) + n(B) − n(A ∩ B)
• "At least one" = n(A ∪ B) — the union
• "Exactly one" = n(A) + n(B) − 2·n(A ∩ B) — union minus the overlap counted twice
• "Neither" = Total − n(A ∪ B)
• "Only A" = n(A) − n(A ∩ B)

For three-set problems, expand to:
n(A ∪ B ∪ C) = n(A) + n(B) + n(C) − n(A ∩ B) − n(B ∩ C) − n(A ∩ C) + n(A ∩ B ∩ C).

Real-world example: A bank's caselet might say "Out of 500 customers visiting Branch X on Monday, 280 used the ATM, 200 used internet banking, 60 used both, and the rest used neither." A Venn instantly tells you: only-ATM = 220, only-internet = 140, both = 60, neither = 500 − 420 = 80.

Common misconception

Common misconception: Many aspirants believe that the trick to caselets is "speed reading." It is not. The trick is slow reading — once, with underlining — followed by fast tabulating. Speed reading makes you miss the linking words, which is exactly where the marks are.

Another common error is mixing up "at least one" with "exactly one." Read both phrases as: at-least-one = union, exactly-one = union − both-region. If you draw the Venn, the diagram itself reminds you which region you are being asked about.

Putting it all together — a SBI PO style mini-caselet

Question: In a society of 1,200 residents, 60% own a car. Of the car-owners, one-third also own a two-wheeler. Among the non-car-owners, 75% own a two-wheeler. How many residents own neither a car nor a two-wheeler?

Solution:
Step 1: Car owners = 60% of 1200 = 720. Non-car owners = 480.
Step 2: Car owners with a two-wheeler = (1/3) × 720 = 240.
Step 3: Non-car owners with a two-wheeler = 75% of 480 = 360. Non-car owners without a two-wheeler = 480 − 360 = 120.
Step 4: Residents owning neither = the 120 non-car owners without a two-wheeler.
Conclusion: 120 residents own neither.

Notice how every sentence in the caselet became one row of arithmetic — that is the conversion habit you are training.

For heavy calculation DI use successive-percentage netting: a rise of a% then b% gives net = a + b + (ab/100). E.g. +10% then +20% = 10+20+2 = +32%. A +20% then −20% = −4% (never zero). For fraction-of-fraction, multiply fractions before touching the base: 3/5 of 2/3 of 900 = (3/5 × 2/3) × 900 = 2/5 × 900 = 360. Digit-sum / first-digit approximation eliminates wrong options fast in 'find approximate value' questions. For ratios that must sum to a total, scale the ratio: if A:B:C = 2:3:5 and total = 4000, each part = 4000/10 = 400, so A=800, B=1200, C=2000. Always reuse the 'one-part value' across the whole question.

Caselet: 'A shop sold 540 items on Day 1. On Day 2 sales rose by 1/3. On Day 3 sales were 90 fewer than Day 2.' Day 2 = 540 × (1 + 1/3) = 540 × 4/3 = 720. Day 3 = 720 − 90 = 630. Total 3-day sales = 540 + 720 + 630 = 1890. 'Day 3 as % of total' = 630/1890 × 100 = 33.33%. 'Average daily sales' = 1890/3 = 630. The discipline: write Day1, Day2, Day3 in a column the moment you read each clause — by the time you finish the paragraph the table is done and every sub-question is a lookup, exactly the SBI PO time-saving habit.

Cover the answer, recall, then check. 12 cards on caselet setup and heavy-calculation DI for SBI PO.

Q1. First thing to do with any caselet?
A1. Transcribe every number into a table or Venn diagram — never solve straight from the paragraph.

Q2. When should you reach for a Venn diagram?
A2. The moment you see "only", "both", "neither", or "all three".

Q3. 60% of a group, then 25% of that — what percent of the original?
A3. 0.6 × 0.25 = 0.15 = 15%. Chain percentages by multiplying, not adding.

Q4. Which quantity should you assign the variable to?
A4. The smallest/base quantity, so the others become clean multiples rather than fractions.

Q5. 60% of 4,800?
A5. 2,880.

Q6. 25% of 2,880?
A6. 720.

Q7. Split 720 in the ratio 5 : 4.
A7. 9 parts → 80 each → 400 and 320.

Q8. Only-A = 30, both = 20, only-B = 25, neither = 25. Total?
A8. 30 + 20 + 25 + 25 = 100.

Q9. For chained percentages, do you add or multiply the fractions?
A9. Multiply — 15% of the original, not 85%.

Q10. When should you skip a caselet?
A10. When the first read doesn't yield a clean frame; its marks-per-minute is poor.

Q11. Formula for n(A ∪ B) in a two-set caselet?
A11. n(A) + n(B) − n(A ∩ B).

Q12. A caselet has two sub-questions — do you re-read for the second?
A12. No. The single frame you built answers both; compute the shared setup once.

A caselet is DI with no chart — the data is buried in a paragraph and your job is to extract it into a table or Venn diagram before solving. SBI PO Mains almost always carries one or two caselets, and they are the highest-difficulty DI because you build the data structure yourself. "Advanced calculation" sets add heavy arithmetic (percentages of percentages, multi-step ratios) on top.

The caselet method

1. Read once for structure: how many entities, what quantities, and what links them.
2. Draw the frame — a small table (rows = entities, columns = quantities) or a Venn diagram for "only/both/all".
3. Translate each sentence into one equation or one filled cell.
4. Solve the lightest unknown first, then back-substitute.

Common caselet types

• Percentage caselet: "A is 20% more than B".
• Ratio caselet: "X : Y = 3 : 5, total 4800".
• Set/Venn caselet: only-A, only-B, both, neither.

Clue (sentence)	Translation
Total candidates = 4800	T = 4800
60% appeared	Appeared = 2880
Of those, 25% qualified	Qualified = 720
Boys : girls qualified = 5 : 4	Boys 400, Girls 320

Example: 60% of 4800 = 2880; 25% of 2880 = 720; 720 split 5 : 4 gives 400 and 320.

Exam Tricks & Tips

• 🎯 Never solve straight from the paragraph — first transcribe every number into a table or diagram.
• 🎯 For "percent of a percent", multiply the fractions (60% then 25% = 0.6 × 0.25 = 15% of the original).
• 🎯 Draw a Venn diagram the instant you see "only", "both", "neither", or "all three".
• 🎯 Assign the variable to the smallest/base quantity so later quantities are multiples, not fractions.
• 🎯 If a caselet has two sub-questions, the frame you build answers both — compute the setup once.
• 🎯 Skip a caselet whose first read won't yield a clean frame; its marks-per-minute is poor.
• ❌ Don't apply successive percentages by adding them — 60% then 25% is 15% of the original, not 85%.

Expected exam pattern

A 3–5 sentence paragraph feeding a 5-question set, or two short caselets. Asks: a derived count, a ratio, a percentage of a derived value, and a difference or total across entities.

Quick recap

Transcribe first, solve second. Build a table or Venn, multiply chained percentages, variable-ise the base quantity, and abandon caselets that won't frame cleanly.