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Age in Years Ago or Years Hence

Introduction

"Age in Years Ago or Years Hence" pattern एक common प्रकार का age-related aptitude problem है। इसमें किसी व्यक्ति की past (years ago) या future (years hence) की age निकालनी होती है, जो उनकी current age या अलग समय पर दी गई age relationship पर आधारित होती है। ऐसे questions में अक्सर statements होते हैं जैसे: "5 years ago, A was twice as old as B" या "10 years hence, A will be 3 times B's age."

Pattern: Age in Years Ago or Years Hence

Pattern

Age problems में आपको अक्सर phrases मिलेंगी जैसे x years ago या x years hence:

x years ago का मतलब होता है कि हम current age में से x subtract करते हैं।
x years hence का मतलब है कि हम current age में x add करते हैं।

इसी तरीके से हम समय में पीछे या आगे जाते हैं।

Past → Subtract years
Future → Add years

ऐसे लिखने पर equations बनाना और solve करना आसान हो जाता है।

Step-by-Step Example

Question

“Five years ago, Rahul was 3 times as old as Neha. यदि Rahul अभी 20 साल का है, तो Neha की present age क्या होगी?”

Options:

  1. 8
  2. 10
  3. 12
  4. 15

Solution

  1. Step 1: Note Rahul’s present age.

    Rahul की present age = 20.

  2. Step 2: Go 5 years back.

    राहुल की age 5 साल पहले = 20 - 5 = 15.

  3. Step 3: Use the condition.

    Question कहता है: Five years ago, Rahul was 3 times Neha’s age.
    इसलिए,
    राहुल की age 5 साल पहले = 3 × (Neha की age 5 साल पहले).
    → 15 = 3 × (Neha’s age 5 years ago).

  4. Step 4: Solve for Neha’s past age.

    Neha की age 5 साल पहले = 15 ÷ 3 = 5.

  5. Step 5: Find Neha’s present age.

    Present age = past age + 5.
    → Neha = 5 + 5 = 10.

  6. Final Answer:

    10 → Option B

  7. Quick Check:

    5 साल पहले → Rahul = 15, Neha = 5.
    Ratio = 15 ÷ 5 = 3 ✅ (condition match करता है)

Quick Variations

अगर question कहे “6 years बाद Rahul Neha का double होगा”, तो equation बनाने से पहले दोनों ages में 6 add करें।

अगर कहा हो “10 years ago, Rahul Neha की आधी age था”, तो दोनों की present ages में से 10 subtract करें और फिर relation बनाएँ।

Trick to Always Use

  1. Step 1: Present ages से शुरुआत करें (या unknown हो तो variables ले लें)।
  2. Step 2: समय में पीछे (-) या आगे (+) जाएँ।
  3. Step 3: दिए गए relation (times, difference, ratio) को apply करें।
  4. Step 4: Solve करें और वापस timeline में रखकर check करें।

Summary

Summary

  • Past age निकालने के लिए present age में से दिए गए years घटाएँ।
  • Future age निकालने के लिए present age में दिए गए years जोड़ें।
  • Equation बनाने से पहले दोनों ages को बराबर years से shift करें।
  • Relation (ratio, times, difference) का उपयोग करके missing age निकालें।

याद रखने लायक बात:
“Past = Current - years, Future = Current + years.”

Practice

(1/5)
1. Five years ago, A was 15 years old. How old is A now?
easy
A. 10
B. 15
C. 20
D. 25

Solution

  1. Step 1: Translate the condition.

    Five years ago A’s age = 15.

  2. Step 2: Add 5 years to get present age.

    Present age = 15 + 5 = 20.

  3. Final Answer:

    20 → Option C

  4. Quick Check:

    20 - 5 = 15 ✅
Hint: For 'x years ago', add x to the given past age to get present age.
Common Mistakes: Subtracting again instead of adding when moving from past to present.
2. Ten years hence, B will be 25 years old. What is B’s current age?
easy
A. 15
B. 20
C. 25
D. 30

Solution

  1. Step 1: Translate the condition.

    10 years hence B = 25.

  2. Step 2: Subtract 10 to get present age.

    Present age = 25 - 10 = 15.

  3. Final Answer:

    15 → Option A

  4. Quick Check:

    15 + 10 = 25 ✅
Hint: For 'x years hence', subtract x from the future age to find present age.
Common Mistakes: Adding instead of subtracting when working backward from a future age.
3. Four years ago, the age of C was 12. What will be C’s age after 6 years from now?
easy
A. 14
B. 16
C. 18
D. 22

Solution

  1. Step 1: Find present age.

    Four years ago C = 12 → Present = 12 + 4 = 16.

  2. Step 2: Move forward 6 years.

    Future = 16 + 6 = 22.

  3. Final Answer:

    22 → Option D

  4. Quick Check:

    16 - 4 = 12 and 16 + 6 = 22 ✅
Hint: Step-by-step: past → present → future.
Common Mistakes: Jumping directly from past to future without computing the present age.
4. Eight years ago, the ratio of D’s age to E’s age was 2 : 3. If D is now 24 years old, what is E’s current age?
medium
A. 28
B. 32
C. 36
D. 40

Solution

  1. Step 1: Find D’s age 8 years ago.

    D now = 24 → D eight years ago = 24 - 8 = 16.

  2. Step 2: Use ratio 2:3.

    If D = 2k → 2k = 16 → k = 8. Then E (8 years ago) = 3k = 24.

  3. Step 3: Move forward 8 years for present E.

    E now = 24 + 8 = 32.

  4. Final Answer:

    32 → Option B

  5. Quick Check:

    Eight years ago: 16 : 24 = 2 : 3 ✅
Hint: Convert to 'then' ages, find k from ratio, then shift to present.
Common Mistakes: Applying ratio to current ages without shifting back to the referenced time.
5. Six years hence, F will be 5 years older than twice G’s present age. If G is currently 10, what will be F’s age after 6 years?
medium
A. 20
B. 25
C. 30
D. 35

Solution

  1. Step 1: Translate the statement.

    Six years hence, F = 2 × (G's present age) + 5.

  2. Step 2: Substitute G = 10.

    F (after 6 years) = 2 × 10 + 5 = 25.

  3. Final Answer:

    25 → Option B

  4. Quick Check:

    Expression directly matches the given relation ✅
Hint: Carefully note whether the relation uses present age of the other person or their future age.
Common Mistakes: Incorrectly adding 6 to G before doubling (the statement uses G's present age).

Mock Test

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