📚 Complete FIA Test Preparation Suite
🎯 One-stop resource for FIA 2026 exam. Master every section with our subject-wise high-yield MCQs, concept anchors, and trap-breaking strategies. Choose your subject below and start your preparation today.
FIA Test Preparation 2026 Main Hub
Complete roadmap, syllabus & strategy
Pakistan Studies MCQs
Constitutional, history, geography & current affairs
Islamiyat MCQs
Quran, Hadith, pillars & Islamic principles
FIA Act 1974 MCQs
Legal framework, powers & investigation rules
English MCQs
Grammar, vocabulary, comprehension & sentence correction
General Knowledge MCQs
World affairs, sports, awards & daily news
Science MCQs
Physics, chemistry, biology & everyday science
⭐ Pro tip: Combine all subjects + our math chapters (Algebra, Percentages, Geometry, Reasoning) for a guaranteed high score in FIA 2026.
📘 PAKSINFO.COM · FIA ENTRY TEST
✏️ Algebra & Word Problems
Simple steps · Smart tricks · No confusion — just marks
🧩
Algebra is just a “translation game”
Every word problem tells a story. Your job: turn that story into a simple equation. Once you write the equation, solving it is just basic math. In FIA test, 6–10 marks come from these 5 patterns.
💡 Golden rule: Read → Find unknown → Write equation → Solve → Verify.
📍 Example: “A number plus 7 equals 15” → x + 7 = 15 → x = 8.
📍 Example: “A number plus 7 equals 15” → x + 7 = 15 → x = 8.
📦 5 Power Formulas (Memorize these)
🔹 Linear (one variable)
If ax + b = c → x = (c – b)/a
Example: 2x+3=11 → 2x=8 → x=4
If ax + b = c → x = (c – b)/a
Example: 2x+3=11 → 2x=8 → x=4
🔹 Age problems
“In 5 years” → add 5 to both ages.
“5 years ago” → subtract 5 from both.
“In 5 years” → add 5 to both ages.
“5 years ago” → subtract 5 from both.
🔹 Heads & Feet
Animals: heads = total count
2×two‑legs + 4×four‑legs = total feet
Animals: heads = total count
2×two‑legs + 4×four‑legs = total feet
🔹 Sum & Difference
Larger = (sum+diff)/2
Smaller = (sum−diff)/2
Larger = (sum+diff)/2
Smaller = (sum−diff)/2
🔹 Venn Diagram (Neither)
Neither = Total − A − B + Both
Neither = Total − A − B + Both
🔹 Work rate (Pipes)
1/timeA + 1/timeB = 1/totalTime
1/timeA + 1/timeB = 1/totalTime
🎯 Easy Examples – Learn Step by Step
📌 Example 1: Linear equation (Fractions? No problem!)
Solve: x/2 – x/3 = 16
✅ Step 1: LCM of 2 and 3 = 6. Multiply every term by 6 → 3x – 2x = 96.
✅ Step 2: x = 96.
✨ Check: 96/2=48, 96/3=32, 48-32=16 ✓
Solve: x/2 – x/3 = 16
✅ Step 1: LCM of 2 and 3 = 6. Multiply every term by 6 → 3x – 2x = 96.
✅ Step 2: x = 96.
✨ Check: 96/2=48, 96/3=32, 48-32=16 ✓
🐔 Example 2: Heads & Feet (Farm animals)
Farmer has roosters (2 legs) and buffaloes (4 legs). 48 heads, 146 feet. Find roosters.
Let r = roosters, b = buffaloes.
r + b = 48 (heads)
2r + 4b = 146 (feet)
Multiply first eq by 2: 2r+2b=96. Subtract from feet eq: (2r+4b) – (2r+2b) = 146-96 → 2b=50 → b=25, so roosters = 23.
🎯 FIA tip: If 23 is not in options, choose “None of these”.
Farmer has roosters (2 legs) and buffaloes (4 legs). 48 heads, 146 feet. Find roosters.
Let r = roosters, b = buffaloes.
r + b = 48 (heads)
2r + 4b = 146 (feet)
Multiply first eq by 2: 2r+2b=96. Subtract from feet eq: (2r+4b) – (2r+2b) = 146-96 → 2b=50 → b=25, so roosters = 23.
🎯 FIA tip: If 23 is not in options, choose “None of these”.
👨👦 Example 3: Age problem (Classic)
Father is 4 times son’s age. In 6 years, father will be 3 times son’s age. Find son’s age.
Let son = s, father = 4s.
In 6 years: (4s+6) = 3(s+6) → 4s+6 = 3s+18 → s = 12. Son is 12.
❗ Mistake alert: Do not forget to add 6 to both ages!
Father is 4 times son’s age. In 6 years, father will be 3 times son’s age. Find son’s age.
Let son = s, father = 4s.
In 6 years: (4s+6) = 3(s+6) → 4s+6 = 3s+18 → s = 12. Son is 12.
❗ Mistake alert: Do not forget to add 6 to both ages!
🍎 Example 4: Sum and Difference (fastest)
Sum of two numbers = 84, difference = 36. Find larger.
Larger = (84 + 36)/2 = 120/2 = 60, smaller = 24.
✅ Direct formula works every time!
Sum of two numbers = 84, difference = 36. Find larger.
Larger = (84 + 36)/2 = 120/2 = 60, smaller = 24.
✅ Direct formula works every time!
☕ Example 5: Venn diagram (People & hobbies)
200 people, 90 like tea, 100 like coffee, 46 like both. How many like neither?
Neither = Total – Tea – Coffee + Both = 200 – 90 – 100 + 46 = 56.
⚠️ Why +46? Because people in “both” were subtracted twice, so add back once.
200 people, 90 like tea, 100 like coffee, 46 like both. How many like neither?
Neither = Total – Tea – Coffee + Both = 200 – 90 – 100 + 46 = 56.
⚠️ Why +46? Because people in “both” were subtracted twice, so add back once.
🚰 Example 6: Work rate (Pipes filling tank)
Pipe A fills in 6 hours, Pipe B in 4 hours. Together?
Rate A = 1/6, Rate B = 1/4 → Combined = 1/6+1/4 = 2/12+3/12 = 5/12.
Total time = 12/5 = 2.4 hours.
✨ Never average the hours: always add rates!
Pipe A fills in 6 hours, Pipe B in 4 hours. Together?
Rate A = 1/6, Rate B = 1/4 → Combined = 1/6+1/4 = 2/12+3/12 = 5/12.
Total time = 12/5 = 2.4 hours.
✨ Never average the hours: always add rates!
⚠️ Avoid These 4 Common Traps
| Trap | Wrong | Correct |
|---|---|---|
| Negative brackets | –(x–4) = –x –4 | –(x–4) = –x +4 |
| Age: add years only to one person | 4x+6 = 3x | 4x+6 = 3(x+6) |
| Venn: forget +Both | 200–90–100 =10 | 200–90–100+46=56 |
| “A is 3 times B” vs “3 more” | A = B+3 (wrong for times) | A = 3B (times) / A = B+3 (more) |
🔥 FIA special trap: 91 is NOT prime (7×13). 97 is prime. Always test division by 2,3,5,7.
📝 Quick Practice – FIA Level MCQs
Click on “Show Answer” after trying each.
⚡ 30‑second Revision Card
- Linear eq: do same to both sides
- Fractions: multiply by LCM
- Age: “in x years” → add to all
- Heads+Feet: multiply heads eq by 2 → subtract
- Venn: Neither = Total – A – B + Both
- Work: 1/t₁ + 1/t₂ = 1/t_total
- Check prime: 97 yes, 91 no
🎯 Remember: Translate first, then solve. FIA algebra is about patterns — you’ve got this!
📘 PAKSINFO.COM · FIA ENTRY TEST
🧮 Percentages & BODMAS
Chapter 2: Arithmetic that earns easy marks — tricks, shortcuts & no confusion
📊 High-Yield Snapshot
Weightage: 5–8 marks🎯 Difficulty: Low to Medium
📆 Trend: 8+ questions in last 3 years (2022–2025)
⚡ Key scenarios: % of a number, % change, BODMAS
🧠 Goal: Solve mentally in under 20 seconds
💡 Gold rule: Percentage means “per hundred”. 10% = move decimal one left. 25% = divide by 4. Master the shortcuts!
📦 Core Formulas & Shortcuts
🔢 Percentage of a number
Part = (Percentage/100) × Whole
10% of 70 = 7 (move decimal)
Part = (Percentage/100) × Whole
10% of 70 = 7 (move decimal)
📈 Percentage Change
% Change = (Difference / OLD value) × 100
Always divide by original!
% Change = (Difference / OLD value) × 100
Always divide by original!
🔄 Find Original
Original = Known × (100 / % it represents)
Example: 30% of salary = 900 → salary = 900 × 100/30 = 3000
Original = Known × (100 / % it represents)
Example: 30% of salary = 900 → salary = 900 × 100/30 = 3000
⚡ Successive % change
Net = x + y + (x·y)/100
Up 20% down 20% → net loss = (20×20)/100 = 4% loss
Net = x + y + (x·y)/100
Up 20% down 20% → net loss = (20×20)/100 = 4% loss
🔁 Consumption reduction
If price rises by x% → reduce consumption by [x/(100+x)]×100%
e.g., 25% rise → cut by 20%
If price rises by x% → reduce consumption by [x/(100+x)]×100%
e.g., 25% rise → cut by 20%
🧮 BODMAS Order
Brackets → Orders → Division/Multiplication (L→R) → Addition/Subtraction
⚠️ 36 ÷ 9 × 4 = 16 (not 1)
Brackets → Orders → Division/Multiplication (L→R) → Addition/Subtraction
⚠️ 36 ÷ 9 × 4 = 16 (not 1)
📌 Must-memorize conversions (FPSC favorite):
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.50 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/3 | 0.333… | 33.33% |
| 2/3 | 0.666… | 66.67% |
| 1/5 | 0.20 | 20% |
| 1/8 | 0.125 | 12.5% |
| 1/10 | 0.10 | 10% |
🎯 Simple Solved Examples (FIA style)
✅ Example 1: 30% of 70
Shortcut: cancel zeros → 3 × 7 = 21. Or 10% of 70 = 7 → 30% = 3×7=21.
Shortcut: cancel zeros → 3 × 7 = 21. Or 10% of 70 = 7 → 30% = 3×7=21.
📈 Example 2: Price rises from 80 to 100 → % increase?
Difference = 20, OLD = 80 → (20/80)×100 = 25% (trap: 20% if divided by new value).
Difference = 20, OLD = 80 → (20/80)×100 = 25% (trap: 20% if divided by new value).
🔁 Example 3: Salary up 20% then down 20%
Net change = – (20×20)/100 = 4% net loss. Verify: 1000 → 1200 → 960 = -40 (4% loss).
Net change = – (20×20)/100 = 4% net loss. Verify: 1000 → 1200 → 960 = -40 (4% loss).
🧾 Example 4: A man spends 65% and saves Rs. 1,750. Salary?
Savings = 35% of salary. Salary = 1750 × (100/35) = 1750 × 20/7 = Rs. 5,000.
⚠️ Trap: using 65% gives wrong answer.
Savings = 35% of salary. Salary = 1750 × (100/35) = 1750 × 20/7 = Rs. 5,000.
⚠️ Trap: using 65% gives wrong answer.
⚙️ Example 5: BODMAS — 36 ÷ 9 × 4
Left to right: 36 ÷ 9 = 4, then 4 × 4 = 16. (Not 1)
Left to right: 36 ÷ 9 = 4, then 4 × 4 = 16. (Not 1)
🍬 Example 6: Sugar price rises 25% → cut consumption to keep expense same
Reduction = [25/(100+25)]×100 = (25/125)×100 = 20%.
Check: old price 100, qty 10 → exp 1000; new price 125, qty 8 → exp 1000.
Reduction = [25/(100+25)]×100 = (25/125)×100 = 20%.
Check: old price 100, qty 10 → exp 1000; new price 125, qty 8 → exp 1000.
⚠️ 5 Deadly Traps (FIA Exam tested)
| Mistake | Wrong | Correct |
|---|---|---|
| Dividing by new value for % change | 20/100 = 20% | 20/80 = 25% |
| Successive % cancel out | +20% then -20% = 0% | 4% net loss |
| BODMAS: multiply first regardless | 36 ÷ 9 × 4 = 36÷36=1 | left to right → 16 |
| Using wrong percentage (spending vs saving) | Salary = 1750×100/65 = 2692 | 1750×100/35 = 5000 |
| “A is 20% more than B” → reverse same % | B is 20% less | B is 16.67% less (20/120×100) |
🧨 Special FPSC traps: √(−25) = imaginary → “None of these”. 91 is NOT prime (7×13). 1/8 = 12.5% (not 12%).
⚡ 30-Second Battle Card
10% → shift decimal
25% = ÷4
% change = (diff/old)×100
Successive net = x+y+xy/100
BODMAS: D/M left to right
Price rise x% → cut by [x/(100+x)]×100
- Up 20% then down 20% = 4% loss
- Down 10% then up 10% = 1% loss
- 1/8 = 12.5% (key fact)
- A is 25% more than B → B is 20% less than A
- √(−25) = none of these
📝 FIA-Level Practice MCQs
Try each question, then click “Show Answer” for explanation.
🔑 Complete Answer Key with Explanations
📘 PAKSINFO.COM · FIA ENTRY TEST
📊 Ratios, Averages & Mixtures
Chapter 3: Easy marks with fixed patterns — master averages, ratios, and mixture removal
📊 High-Yield Snapshot
Weightage: 3–4 marks⚡ Difficulty: Low–Medium
📌 Trend: 6+ questions (2022–2025) – reliable scoring
🎯 Key topics: Averages, ratio division, mixture change, weighted avg
🧠 Strategy: Learn templates → solve in 30 seconds
💡 Golden rule: Average = Sum/Count, Ratio = part-to-part (total parts = sum of ratio numbers). Mixture removal affects ALL components proportionally.
📦 Core Formulas & Shortcuts
📊 Average (Arithmetic Mean)
Average = Sum ÷ Count
Sum = Avg × Count
Missing value = New sum − Old sum
Average = Sum ÷ Count
Sum = Avg × Count
Missing value = New sum − Old sum
🔁 Evenly spaced values
Middle value = Average
Youngest = Avg − (n−1)/2 × d
5 children, 2-yr interval, avg=18 → youngest = 14
Middle value = Average
Youngest = Avg − (n−1)/2 × d
5 children, 2-yr interval, avg=18 → youngest = 14
📐 Simple Ratio
Total parts = sum of ratios
Value of 1 part = Whole ÷ Total parts
Share = ratio number × 1 part
Total parts = sum of ratios
Value of 1 part = Whole ÷ Total parts
Share = ratio number × 1 part
⚖️ Weighted Average
Weighted Avg = (n₁×a₁ + n₂×a₂) ÷ (n₁+n₂)
Never average the averages!
Weighted Avg = (n₁×a₁ + n₂×a₂) ÷ (n₁+n₂)
Never average the averages!
🧪 Mixture (removal)
Remove proportionally from ALL components
Then set up new ratio equation
Remove proportionally from ALL components
Then set up new ratio equation
🚗 Average speed (equal distances)
Harmonic mean = 2×v₁×v₂/(v₁+v₂)
Not the arithmetic mean!
Harmonic mean = 2×v₁×v₂/(v₁+v₂)
Not the arithmetic mean!
🎯 Step-by-Step Solved Examples
✅ Example 1: Basic Average
Sum of 10 values = 10 → Average = 10/10 = 1 (CSS MPT 2022 trap: 10 is wrong).
Sum of 10 values = 10 → Average = 10/10 = 1 (CSS MPT 2022 trap: 10 is wrong).
👧 Example 2: Evenly spaced ages
5 children born 2 years apart, average age 18 → youngest? Middle (3rd) = 18, ages: 14,16,18,20,22 → youngest = 14.
5 children born 2 years apart, average age 18 → youngest? Middle (3rd) = 18, ages: 14,16,18,20,22 → youngest = 14.
📈 Example 3: Missing value when average changes
Mean of 5 obs = 10, add 6th → new mean = 12 → 6th obs = New sum(72) − Old sum(50) = 22.
Mean of 5 obs = 10, add 6th → new mean = 12 → 6th obs = New sum(72) − Old sum(50) = 22.
💰 Example 4: Simple ratio
Rs. 900 divided 2:7 → total parts=9, 1 part=100 → Ali=200, Bilal=700.
Rs. 900 divided 2:7 → total parts=9, 1 part=100 → Ali=200, Bilal=700.
🍎 Example 5: Mixture (removal + addition)
2L juice (1:3 apple:orange), remove 400ml → apple left=400ml, orange left=1200ml. Add apple to get 7:5 → solve (400+x)/1200 = 7/5 → x = 1280 ml → None of these (CSS MPT 2023 special).
2L juice (1:3 apple:orange), remove 400ml → apple left=400ml, orange left=1200ml. Add apple to get 7:5 → solve (400+x)/1200 = 7/5 → x = 1280 ml → None of these (CSS MPT 2023 special).
🏫 Example 6: Weighted average
Class A (30 students, avg 70) + Class B (20 students, avg 80) → combined = (2100+1600)/50 = 74 (not 75).
Class A (30 students, avg 70) + Class B (20 students, avg 80) → combined = (2100+1600)/50 = 74 (not 75).
⚠️ 5 Deadly Traps (FIA Exam)
| Mistake | Wrong Approach | Correct Fix |
|---|---|---|
| Dividing by wrong number | Sum=10, count=10 → avg=10 | avg = 10÷10 = 1 |
| Averaging averages without weighting | (70+80)/2 = 75 | (30×70 + 20×80)/50 = 74 |
| Removing only one component in mixture | Remove 400ml from apple only | Remove proportionally from ALL |
| Ratio: using part as denominator | 2:3 → share = 2/3 of total | total parts = 5 → share = 2/5 of total |
| Average speed = avg of speeds | (30+60)/2 = 45 km/h | harmonic mean = 2×30×60/(90) = 40 km/h |
🧨 Special FPSC traps: “Sum of 10 values = 10” average is 1 (not 10). Middle value shortcut always works for evenly spaced. Mixture removal is proportional. Weighted average leans toward larger group.
⚡ 5-Minute Battle Card
Avg = Sum/Count
Sum = Avg × Count
Missing value = New sum − Old sum
Evenly spaced: middle = average
Total parts = sum of ratios
Weighted avg: multiply by group size
- 5 children, 2-yr interval, avg 18 → youngest 14 (not 16)
- Mixture removal: remove from all components proportionally
- Average speed (equal distance) = 2×v₁×v₂/(v₁+v₂)
- Never choose “None of these” without full calculation
📝 FIA-Level Practice MCQs
Click “Show Answer” after solving each.
🔑 Complete Answer Key with Explanations
📘 PAKSINFO.COM · FIA ENTRY TEST
📐 Geometry Basics
Chapter 4: Lines, Angles, Triangles, Quadrilaterals, Polygons & Circles — pure definition-based scoring
📊 High-Yield Snapshot
Weightage: 4–6 marks⚡ Difficulty: Low (pure memorisation)
📌 Trend: 13+ questions (2022–2025) – reliable scoring
🎯 Key topics: Lines, angles, triangles, quadrilaterals, polygons, circles
🧠 Strategy: Learn definitions & tables → no calculations
💡 Golden rule: Geometry in FIA is a vocabulary test. Every answer is in the tables below. No proofs, no complex formulas — just definitions.
📦 Core Concepts & Definitions
📏 Lines & Endpoints
| Object | Endpoints | Extends infinitely? |
|---|---|---|
| Line | 0 | Both directions |
| Ray | 1 | One direction |
| Line segment | 2 | No (fixed length) |
⚠️ Trap: A geometric line has zero endpoints. Do not confuse with a drawn line segment.
📐 Angle Types
| Angle Type | Measure |
|---|---|
| Acute | 0° – 90° |
| Right | Exactly 90° |
| Obtuse | 90° – 180° |
| Straight | Exactly 180° |
| Reflex | 180° – 360° |
🧠 Complementary & Supplementary
Complementary → sum = 90° (Corner)
Supplementary → sum = 180° (Straight)
Complementary → sum = 90° (Corner)
Supplementary → sum = 180° (Straight)
🔺 Triangles
| Type | Properties |
|---|---|
| Equilateral | All 3 sides equal & all angles equal (60° each) – BOTH |
| Isosceles | 2 sides equal, 2 base angles equal |
| Scalene | All sides different |
| Right-angled | One angle = 90° (Pythagoras: a²+b²=c²) |
| Acute-angled | All angles < 90° |
| Obtuse-angled | One angle > 90° |
📐 Pythagorean triples (memorise): 3-4-5, 5-12-13, 8-15-17
⬛ Quadrilaterals
| Shape | Properties |
|---|---|
| Square | All 4 sides equal & all angles = 90° |
| Rectangle | Opposite sides equal, all angles = 90° |
| Parallelogram | Opposite sides equal & parallel |
| Rhombus | All 4 sides equal, angles not 90° |
| Trapezium | Only one pair of parallel sides |
🟢 Polygons (sides & interior angle sum)
| Name | Sides | Sum of interior angles |
|---|---|---|
| Triangle | 3 | 180° |
| Quadrilateral | 4 | 360° |
| Pentagon | 5 | 540° |
| Hexagon | 6 | 720° |
| Heptagon | 7 | 900° |
| Octagon | 8 | 1080° |
| Nonagon | 9 | 1260° |
| Decagon | 10 | 1440° |
📐 Polygons: Sum of interior angles = (n−2)×180°.
Sum of exterior angles = 360° (always).
Sum of exterior angles = 360° (always).
⚪ Circles
| Term | Definition |
|---|---|
| Radius (r) | Centre to any point on circle |
| Diameter (d) | 2×r, longest chord |
| Chord | Segment joining two points on circumference |
| Circumference | Perimeter = 2πr = πd |
| Area | πr² |
| Tangent | Touches circle at exactly one point |
⚠️ Longest chord = Diameter (circumference is NOT a chord).
Hollow cylinder surface area (open both ends) = 2πrh (curved only).
Hollow cylinder surface area (open both ends) = 2πrh (curved only).
🎯 Step-by-Step Solved Examples
✅ Example 1: Endpoints of a line
How many endpoints does a line have? 0 (extends infinitely). Line segment: 2, Ray: 1.
How many endpoints does a line have? 0 (extends infinitely). Line segment: 2, Ray: 1.
📐 Example 2: Complementary angles
Complementary sum = 90°. Supplementary = 180°.
Complementary sum = 90°. Supplementary = 180°.
🔺 Example 3: Equilateral triangle
All sides equal AND all angles equal (both properties). FPSC trap: separate options.
All sides equal AND all angles equal (both properties). FPSC trap: separate options.
⬛ Example 4: Quadrilateral with all four sides equal
Square (also rhombus, but only square has 90° angles). From given options: Square.
Square (also rhombus, but only square has 90° angles). From given options: Square.
⚪ Example 5: Longest chord of a circle
Diameter – not circumference (circumference is the perimeter).
Diameter – not circumference (circumference is the perimeter).
🟢 Example 6: Octagon
8 sides → Octagon (Octa = 8).
8 sides → Octagon (Octa = 8).
🧴 Example 7: Hollow cylinder surface area
Curved surface only = 2πrh (no top/bottom).
Curved surface only = 2πrh (no top/bottom).
📐 Example 8: Pythagoras theorem
Legs 3 & 4 → hypotenuse = 5 (3-4-5 triple).
Legs 3 & 4 → hypotenuse = 5 (3-4-5 triple).
⚠️ 5 Deadly Traps (FIA Exam)
| Mistake | Wrong | Correct |
|---|---|---|
| Line vs Line segment | Line has 2 endpoints | Line has 0 endpoints |
| Complementary vs Supplementary | Complementary = 180° | Complementary = 90° (Corner) |
| Longest chord of circle | Circumference | Diameter |
| Rectangle vs Square | All sides equal → Rectangle | All sides equal → Square |
| Equilateral triangle | Only sides equal | Both sides & angles equal |
🧨 Special FPSC confirmed: Vertex is the point where two rays meet. Sum of exterior angles of any polygon = 360°. Hollow cylinder area = 2πrh (appeared twice in same paper).
⚡ 5-Minute Battle Card
Line: 0 endpoints
Complementary = 90°
Equilateral: both sides & angles
Longest chord = diameter
Polygon sides: Octagon=8
Sum exterior angles = 360°
- Hollow cylinder surface area = 2πrh
- Pythagoras triples: 3-4-5, 5-12-13, 8-15-17
- Sum interior angles = (n-2)×180°
- Vertex: where two rays meet
📝 FIA-Level Practice MCQs
Click “Show Answer” after solving each.
🔑 Complete Answer Key with Explanations
📘 PAKSINFO.COM · FIA ENTRY TEST
🧩 Blood Relations, Rankings, Seating & Directions
Chapter 5: Solve with diagrams — never hold relationships in your head
📊 High-Yield Snapshot
Weightage: 3–5 marks⚡ Difficulty: Low–Medium
📌 Trend: Consistent 3–5 marks across all papers
🎯 Four types: Ranking, Seating, Direction, Blood relations
🧠 Golden rule: Draw first, answer second
💡 Universal strategy: Every problem type becomes visual — chain for rankings, row for seating, compass for directions, family tree for blood relations. Without the diagram, you will get confused.
📦 The Four Problem Types
🥇 Type 1: Ranking & Comparison
Method: Build a chain: A > B > C. If any person has no stated relationship → answer is “Cannot be determined”.
🔹 Example: C has more than D but less than A → A > C > D. B unplaced → cannot know highest.
🪑 Type 2: Seating Arrangement
Method: Draw blank seats: _ _ _ _. Place most constrained person first. “X to the right of Y” → Y … X (left to right).
🔹 Example: 5 seats, ends fixed, middle conditions → draw row step by step.
🧭 Type 3: Direction & Rotation
Turn Rules: Right (CW): N→E→S→W→N. Left (CCW): N→W→S→E→N. U-turn: N↔S, E↔W.
Shadows: Morning (East sun) → shadow West. Evening (West sun) → shadow East. Noon → shadow North.
Shadows: Morning (East sun) → shadow West. Evening (West sun) → shadow East. Noon → shadow North.
👨👩👧 Type 4: Blood Relations
Method: Draw a family tree. Never calculate mentally.
| Relation phrase | Meaning |
|---|---|
| Father/Mother’s brother | Uncle |
| Father/Mother’s sister | Aunt |
| Brother/Sister’s son | Nephew |
| Brother/Sister’s daughter | Niece |
| “Father’s only son” (by a woman) | Her brother |
| “Mother’s only daughter” (by a man) | His sister |
🎯 Step-by-Step Solved Examples
✅ Example 1 (Ranking): P, Q, R, S heights. R > S, P > R. Who is tallest? Chain: P > R > S. Q unplaced → Cannot be determined.
✅ Example 2 (Seating): Five persons A,B,C,D,E. B immediate right of A. D at end. C between E and B. E not at ends. Arrive at: A B C E D → middle = C.
✅ Example 3 (Direction walk): Faces North, walks 4km, turns right (East), 3km, turns right (South). Now facing South, distance = √(4²+3²)=5km.
✅ Example 4 (Shadow): At 7 AM, Sun East → shadow West. Person faces shadow → faces West.
✅ Example 5 (Blood relation): Woman says “He is son of my father’s only son”. Father’s only son = her brother. Brother’s son = nephew. She is aunt.
✅ Example 6 (Rotation): NE → N (45° CCW), NW → W (same shift). West → SW.
⚠️ 5 Deadly Traps (FIA Exam)
| Mistake | Wrong | Correct |
|---|---|---|
| Assuming known chain top is overall highest | A is tallest (ignores B) | Cannot be determined if any person unplaced |
| Confusing left/right in seating | X right of Y → draw X … Y | Y … X (X after Y left→right) |
| Turning wrong direction | North turn right → West | North turn right → East (CW) |
| Father’s only son = self (woman speaker) | She thinks it’s herself | It’s her brother |
| Shadow direction = in front/behind | “Shadow is behind me” | Answer is compass direction (East/West/North) |
🧨 Special FPSC traps: Unplaced person in ranking → “Cannot be determined”. Typo or missing reference → “None of these”. CSS MPT 2023 had “R is left of A” with no A defined → answer = None of these.
⚡ 5-Minute Battle Card
Ranking: chain + check unplaced
Seating: draw blanks first
Direction: compass always
Blood: family tree
- Right turn = clockwise (N→E→S→W)
- Morning shadow = West, Evening shadow = East
- “Father’s only son” (woman) = brother
- Unplaced person → Cannot be determined
- Row rank: Total = top + bottom – 1
📝 FIA-Level Practice MCQs
Click “Show Answer” after solving each.