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Conditional Statements in Age

Introduction

कुछ age problems में direct age नहीं दी होती, बल्कि conditions के रूप में जानकारी दी जाती है। जैसे: "Rahul is twice as old as Neha" या "After 5 years, father will be 3 times the son’s age"। ऐसे questions को Conditional Statement age problems कहा जाता है।

इनको solve करने की key है: unknown ages को variables assign करना और हर sentence को एक clear equation में बदलना। यह करने के बाद पूरा solution बहुत आसान हो जाता है।

Pattern: Conditional Statements in Age

Pattern

मुख्य idea:

Unknown age (आमतौर पर सबसे छोटे की age) को एक variable दें।

Question के हर sentence को दिए गए condition के अनुसार equation में बदलें।

इन equations को solve करके required ages निकालें।

Step-by-Step Example

Question

Rahul, twice as old as Neha है। 5 years बाद वह Neha से 3 years older होगा। उनकी present ages निकालें।

Options:

  • A: Neha = 3 years, Rahul = 6 years
  • B: Neha = 4 years, Rahul = 8 years
  • C: Neha = 5 years, Rahul = 10 years
  • D: Neha = 6 years, Rahul = 12 years

Solution

  1. Step 1: Variables assign करें।

    Neha की present age = x
    Rahul की present age = 2x (क्योंकि वह Neha से twice है)

  2. Step 2: Future condition को translate करें।

    5 साल बाद:
    Neha = x + 5
    Rahul = 2x + 5
    Condition: 2x + 5 = (x + 5) + 3

  3. Step 3: Equation solve करें।

    2x + 5 = x + 8
    x = 3

  4. Step 4: Actual ages निकालें।

    Neha = 3 years
    Rahul = 6 years

  5. Final Answer:

    Neha = 3 years, Rahul = 6 years → Option A

  6. Quick Check:

    5 साल बाद: Neha = 8, Rahul = 11 → difference = 3 years ✅

Quick Variations

Conditional statements में past ages, future ages, या multiples of ages शामिल हो सकते हैं। Method हमेशा वही रहता है: variable assign → condition translate → equation solve.

Trick to Always Use

  • Step 1: Unknown age को variable दें।
  • Step 2: हर condition को equation में बदलें।
  • Step 3: ध्यान से solve करें।
  • Step 4: Original condition से verify करें।

Summary

Summary

  • Unknown को पहचानें और variable दें।
  • Conditional statements को सही equation में translate करें।
  • Step-by-step solve करें और ages निकालें।
  • Values को वापस condition में रखकर verify करें।

याद रखने का तरीका: Assign variable → Translate → Solve → Verify

Practice

(1/5)
1. If X is older than Y and their total is 30, and Y is 10, find X’s age.
easy
A. 18
B. 20
C. 22
D. 25

Solution

  1. Step 1: Translate the condition.

    X + Y = 30 and Y = 10.

  2. Step 2: Solve for X.

    X = 30 - 10 = 20.

  3. Final Answer:

    20 → Option B

  4. Quick Check:

    20 + 10 = 30 ✅
Hint: Subtract the known age from the total.
Common Mistakes: Adding instead of subtracting.
2. If A is twice B and their total is 36, find A and B.
easy
A. 24 and 12
B. 20 and 16
C. 18 and 18
D. 28 and 8

Solution

  1. Step 1: Translate the condition.

    A = 2B and A + B = 36.

  2. Step 2: Substitute and solve.

    2B + B = 36 → 3B = 36 → B = 12.

  3. Step 3: Find A.

    A = 2 × 12 = 24.

  4. Final Answer:

    A = 24, B = 12 → Option A

  5. Quick Check:

    24 + 12 = 36 ✅
Hint: Replace A with 2B in the total equation.
Common Mistakes: Forgetting to substitute correctly before solving.
3. If P is 5 years older than Q and the sum is 35, find P and Q.
medium
A. 20 and 15
B. 18 and 17
C. 22 and 13
D. 25 and 10

Solution

  1. Step 1: Write equations.

    P = Q + 5 and P + Q = 35.

  2. Step 2: Substitute and solve.

    (Q + 5) + Q = 35 → 2Q + 5 = 35 → Q = 15.

  3. Step 3: Find P.

    P = 15 + 5 = 20.

  4. Final Answer:

    P = 20, Q = 15 → Option A

  5. Quick Check:

    20 + 15 = 35 ✅
Hint: Express older person as younger + difference.
Common Mistakes: Using P = Q - 5 instead of Q + 5.
4. If a father is 3 times his son and their sum is 48, find their ages.
medium
A. 36 and 12
B. 30 and 18
C. 34 and 14
D. 40 and 8

Solution

  1. Step 1: Translate the condition.

    F = 3S and F + S = 48.

  2. Step 2: Substitute and solve.

    3S + S = 48 → 4S = 48 → S = 12.

  3. Step 3: Find father’s age.

    F = 3 × 12 = 36.

  4. Final Answer:

    Father = 36, Son = 12 → Option A

  5. Quick Check:

    36 + 12 = 48 ✅
Hint: Let the younger person be the variable when the elder is a multiple.
Common Mistakes: Wrong assumption like F = S/3 instead of F = 3S.
5. If A is 4 times B and B is 6 years old, find A’s age.
medium
A. 20
B. 22
C. 24
D. 26

Solution

  1. Step 1: Translate the relationship.

    A = 4B, B = 6.

  2. Step 2: Solve for A.

    A = 4 × 6 = 24.

  3. Final Answer:

    24 → Option C

  4. Quick Check:

    24 ÷ 6 = 4 ✅
Hint: Multiply when direct multiple relation is given.
Common Mistakes: Dividing instead of multiplying.

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