Coding-Decoding & Mathematical Relationships

Coding किसी word, letter, number या symbol को एक specific rule (कूट) के अनुसार दूसरे रूप में बदलना है।

Decoding coded form से original form को खोजना है।

Key Point: UGC NET में coding-decoding questions pattern recognition और logical reasoning को test करते हैं।

Types of Coding-Decoding:

• Letter Coding — अक्षर कूट: Letters को एक rule के अनुसार बदलना
• Number Coding — संख्या कूट: Numbers को code में बदलना
• Mixed Coding — मिश्रित कूट: Letters और numbers का combination
• Substitution Coding — प्रतिस्थापन कूट: One word/symbol को another से replace करना
• Decoding — कूट-पठन: Code से original word खोजना

Letter Coding में letters को alphabet positions के अनुसार बदला जाता है।

Common Patterns:

• Direct Addition/Subtraction: +2, −3, etc.
• Reverse Alphabet: A↔Z, B↔Y, C↔X (sum = 27)
• Increasing/Decreasing Differences: +1, +2, +3...
• Vowel/Consonant Patterns
• Positional Swapping

Example 1:

• If CAT is coded as DDU (C→D = +1, A→D = +3, T→U = +1)
• Then DOG = ?
• D→E = +1, O→R = +3, G→H = +1 → ERH

Example 2:

• If MAN is coded as NZM (M→N = +1, A→Z = −1, N→M = −1)

Reverse Alphabet Coding:

• If CAT is coded as XZG (C↔X, A↔Z, T↔G)
• Opposite letter sum = 27 (C=3 → X=24, 3+24=27)

Number Coding में letters को numbers में बदला जाता है (alphabet positions का उपयोग).

Example 1:

• If CAT is coded as 3120 (C=3, A=1, T=20)
• Then DOG = ?
• D=4, O=15, G=7 → 4157

Example 2:

• If BALL is coded as 211212 (B=2, A=1, L=12, L=12)
• Then CALL = ?
• C=3, A=1, L=12, L=12 → 311212

Example 3 (Sum of Positions):

• If CAT is coded as 24 (3+1+20=24)
• Then DOG = ?
• D=4, O=15, G=7 → 4+15+7=26

Mixed Coding में letters और numbers दोनों का combination use होता है या pattern complex होता है।

Example 1:

• If CAT is coded as C3T (vowels replaced by position, consonants unchanged)
• Then DOG = ?
• D, O=15, G → D15G

Example 2:

• If BAT is coded as 2B3T (first letter position, original, third letter position...)

Example 3 (Difference Coding):

• If CAT is coded as 3-1-20 (positions with hyphens)
• Then DOG = 4-15-7

Substitution Coding में एक word या symbol को दूसरे word या symbol से replace (बदल) दिया जाता है।

Example:

• If 'red' is called 'blue', 'blue' is called 'green', and 'green' is called 'yellow'.
• Question: What is the colour of blood?
• Blood is red → but red is called blue → Answer: Blue

Key Point: Substitution coding में carefully follow the substitution chain.

Decoding coded form से original word/meaning को खोजना है।

Example:

• If 3120 is code for CAT (3=C, 1=A, 20=T)
• What is 4157?
• 4=D, 15=O, 7=G → DOG

Strategy:

• Identify the coding rule from the given example(s)
• Apply the same rule to decode the given code
• Work backwards from code to original

Mathematical Relationships questions में numbers और their relationships (age, ratio, proportion, percentage, time & work, speed & distance) पर आधारित problems होते हैं।

Common Topics:

• Age Problems — आयु संबंधी
• Ratio & Proportion — अनुपात एवं समानुपात
• Percentage — प्रतिशत
• Time & Work — समय एवं कार्य
• Speed & Distance — चाल एवं दूरी

Key Formulae:

• Present Age: Let present age = x
• Age n years ago: x − n
• Age n years hence: x + n
• Ratio of ages: Use ratio to form equations

Example:

• A is 5 years older than B. After 3 years, A's age will be twice B's age. Find their present ages.
• Let B's age = x → A's age = x + 5
• After 3 years: (x+5)+3 = 2(x+3)
• x+8 = 2x+6 → x = 2
• B = 2, A = 7

Tip: Always form equations using the given relationships.

Key Formulae:

• a : b = c : d → a × d = b × c (Cross multiplication)
• Ratio of two quantities: a : b = (a/b)
• If a:b and b:c are given: a:b:c = (a×b) : (b×b) : (b×c)
• Shared amount in ratio: Total × (share ratio / total ratio)

Example:

• ₹500 is divided between A and B in ratio 2:3. How much does each get?
• Total ratio = 2+3 = 5
• A = 500 × 2/5 = 200
• B = 500 × 3/5 = 300

Key Formulae:

• X% of Y: (X/100) × Y
• Percentage Increase: (Increase / Original) × 100
• Percentage Decrease: (Decrease / Original) × 100
• New Value after Increase: Original × (100 + X%) / 100
• New Value after Decrease: Original × (100 − X%) / 100

Example:

• What is 25% of 400? → (25/100) × 400 = 100
• If a price increases from ₹200 to ₹250, what is the percentage increase?
• Increase = 50, Original = 200 → (50/200) × 100 = 25%

Key Formulae:

• If A can do work in x days: A's 1 day work = 1/x
• If A and B together: (1/x + 1/y) work in 1 day
• Time taken together: 1/(1/x + 1/y) = xy/(x+y)
• If A is n times efficient than B: Time ratio = A:B = 1:n

Example:

• A can do work in 10 days, B can do it in 15 days. How long will they take together?
• A's 1 day = 1/10, B's 1 day = 1/15
• Together = 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6
• Time = 6 days

Key Formulae:

• Average Speed = Total Distance / Total Time
• If distances are same: Average Speed = 2xy/(x+y) (where x and y are speeds)
• Conversion: km/h to m/s → multiply by 5/18; m/s to km/h → multiply by 18/5

Example:

• A car travels 60 km at 30 km/h and 60 km at 60 km/h. Find average speed.
• Time1 = 60/30 = 2 hours; Time2 = 60/60 = 1 hour
• Total distance = 120 km, Total time = 3 hours
• Average speed = 120/3 = 40 km/h

• Age: Present = x, n years ago = x−n, n years hence = x+n
• Ratio: a:b = a/b, a:b:c = a×b : b×b : b×c
• Proportion: a:b::c:d → ad = bc
• Percentage: (Part/Whole) × 100
• Time & Work: 1 day work = 1/n, Together = xy/(x+y)
• Speed & Distance: S = D/T, Avg Speed = Total D/Total T
• Average Speed (same distance): 2xy/(x+y)

• Trap 1: Letter coding = always +/− constant → ❌ Patterns can vary (increasing differences, reverse, positional, mixed).
• Trap 2: Number coding = just alphabet positions → ❌ It can also be sum, difference, product, or mixed operations.
• Trap 3: Substitution coding = direct translation → ❌ Follow the substitution chain carefully.
• Trap 4: Age problems = always linear → ❌ May include ratios, sums, differences, and multiple people.
• Trap 5: Ratio = exact numbers → ❌ Ratio is a relation, not actual numbers.
• Trap 6: Percentage increase = percentage decrease → ❌ Different bases (original vs new).
• Trap 7: Time & Work = just add times → ❌ Add rates, not times.

If CAT is coded as DDU, what is DOG coded as?

• A. ERH
• B. EPI
• C. ERI
• D. EPH

Explanation: C→D (+1), A→D (+3), T→U (+1). Apply same: D→E (+1), O→R (+3), G→H (+1) → ERH.

If BAT is coded as 2120, what is CAT coded as?

• A. 3120
• B. 3210
• C. 3119
• D. 2119

Explanation: BAT: B=2, A=1, T=20 → 2120. CAT: C=3, A=1, T=20 → 3120.

If 4157 is code for DOG (4=D, 15=O, 7=G), what is 31820?

• A. CAT
• B. CAR
• C. CAN
• D. CAP

Explanation: 3=C, 18=R, 20=T → 3-18-20 is not in options. 3=C, 1=A, 18=R → CAR (3, 1, 18).

A is 10 years older than B. After 5 years, A's age will be twice B's age. Find B's present age.

• A. 5
• B. 8
• C. 10
• D. 12

Explanation: Let B = x, A = x+10. After 5 years: (x+10)+5 = 2(x+5) → x+15 = 2x+10 → x = 5.

Divide ₹1200 between A and B in ratio 3:5. How much does B get?

• A. 450
• B. 600
• C. 720
• D. 750

Explanation: Total ratio = 3+5=8. B = 1200 × 5/8 = 750.

What is 30% of 250?

• A. 60
• B. 75
• C. 80
• D. 90

Explanation: (30/100) × 250 = 75.

A can do work in 6 days, B in 12 days. How many days will they take together?

• A. 3
• B. 4
• C. 6
• D. 8

Explanation: A's 1 day = 1/6, B's = 1/12. Together = 1/6 + 1/12 = 2/12 + 1/12 = 3/12 = 1/4 → Time = 4 days.

Coding-Decoding Types:

• Letter Coding (A=1, B=2...)
• Number Coding (positions)
• Mixed Coding (letters + numbers)
• Substitution Coding (replacements)
• Decoding (reverse process)

Mathematical Relationships Formulae:

• Age: Present = x, x±n for ago/hence
• Ratio: a:b = a/b
• Percentage: (Part/Whole) × 100
• Time & Work: 1 day work = 1/n; Together = xy/(x+y)
• Speed & Distance: S = D/T; Avg S = Total D/Total T

Exam Formula:

UGC NET में Coding-Decoding और Mathematical Relationships के questions logical thinking और basic arithmetic skills को test करते हैं।