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Age Sum Given

Introduction

कुछ aptitude problems में difference या ratio देने की बजाय, सीधे sum of present ages दिया होता है। इस information को किसी दूसरी condition के साथ मिलाकर equations बनाई जाती हैं, और actual ages निकाली जाती हैं।

ऐसे questions बहुत आसान होते हैं यदि आप conditions को सही तरह से equations में बदलें। आइए इस pattern को एक clear example के साथ समझते हैं।

Pattern: Age Sum Given

Pattern

मुख्य विचार:

यदि A और B की ages का sum दिया है, तो लिखते हैं:
A + B = (given value)

फिर दूसरी condition (ratio, difference, relation) की मदद से sum को actual ages में split किया जाता है।

Step-by-Step Example

Question

Rahul और Neha की present ages का sum 50 years है। Rahul, Neha से 4 साल बड़ा है। उनकी present ages ज्ञात करें।

Options:

  • A: Rahul 27, Neha 23
  • B: Rahul 26, Neha 24
  • C: Rahul 28, Neha 22
  • D: Rahul 25, Neha 25

Solution

  1. Step 1: Represent the ages.

    “Rahul is 4 years older than Neha” → Neha की present age = N Rahul की present age = N + 4

  2. Step 2: Use the sum condition.

    Sum = 50 → N + (N + 4) = 50 → 2N + 4 = 50

  3. Step 3: Solve the equation.

    2N + 4 = 50 → 2N = 46 → N = 23

  4. Step 4: Find Rahul’s age.

    Rahul = N + 4 = 23 + 4 = 27

  5. Final Answer:

    Rahul = 27, Neha = 23 → Option A

  6. Quick Check:

    23 + 27 = 50 ✅

Quick Variations

यदि difference की जगह दूसरी condition ratio हो (जैसे “ratio = 3:2”), तो sum को सीधे ratio parts में split करें।

उदाहरण: Sum = 50, ratio = 3:2 → total parts = 5 → 1 part = 10 → Ages = 30 और 20.

Trick to Always Use

  • Step 1: Ages को variables से represent करें।
  • Step 2: Sum condition को apply करें।
  • Step 3: दूसरी condition (difference/ratio) से sum को split करें।
  • Step 4: Solve करें और verify करें।

Summary

Summary

Age Sum Given pattern में sum को किसी दूसरी condition (difference या ratio) के साथ जोड़कर actual ages निकाली जाती हैं।

  • Step 1: A + B = (given sum) लिखें।
  • Step 2: Extra condition से दूसरा equation बनाएं।
  • Step 3: Ages solve करें।
  • Step 4: Sum दोबारा check करें।

Master कर लेने पर sum-based age problems बहुत जल्दी solve हो जाते हैं!

Practice

(1/5)
1. The sum of Rahul's and Neha's ages is 50 years. If Rahul is 30 years old, what is Neha's age?
easy
A. 20
B. 30
C. 25
D. 15

Solution

  1. Step 1: Translate the sentence.

    The sum of Rahul and Neha = 50; Rahul = 30.

  2. Step 2: Use the sum to find Neha.

    Neha = 50 - 30 = 20.

  3. Final Answer:

    20 → Option A

  4. Quick Check:

    30 + 20 = 50 ✅
Hint: Subtract the known age from the total to get the other age.
Common Mistakes: Swapping ages or subtracting in the wrong order.
2. The total age of 3 sisters is 48 years. Two of them are 14 and 15 years old. What is the age of the third sister?
easy
A. 20
B. 19
C. 21
D. 18

Solution

  1. Step 1: Translate the sentence.

    Total of three sisters = 48; two ages = 14 and 15.

  2. Step 2: Subtract known ages from the total.

    Third = 48 - (14 + 15) = 48 - 29 = 19.

  3. Final Answer:

    19 → Option B

  4. Quick Check:

    14 + 15 + 19 = 48 ✅
Hint: Add the known ages first, then subtract from the total.
Common Mistakes: Forgetting to add the known ages correctly before subtracting.
3. Four friends have a total age of 80 years. Three are 18, 21 and 17. Find the fourth friend's age.
easy
A. 22
B. 25
C. 24
D. 20

Solution

  1. Step 1: Translate the sentence.

    Total of 4 friends = 80; three ages = 18, 21, 17.

  2. Step 2: Sum known ages and subtract.

    Sum known = 18 + 21 + 17 = 56. Fourth = 80 - 56 = 24.

  3. Final Answer:

    24 → Option C

  4. Quick Check:

    18 + 21 + 17 + 24 = 80 ✅
Hint: Group additions first, then subtract from total to minimize errors.
Common Mistakes: Arithmetic errors when adding several ages.
4. The sum of ages of A and B is 50 years. A is 4 years older than B. Find their present ages.
medium
A. A 26, B 24
B. A 28, B 22
C. A 29, B 21
D. A 27, B 23

Solution

  1. Step 1: Translate to equations.

    A + B = 50 and A = B + 4.

  2. Step 2: Substitute and solve.

    (B + 4) + B = 50 → 2B + 4 = 50 → 2B = 46 → B = 23. Then A = 23 + 4 = 27.

  3. Final Answer:

    A = 27, B = 23 → Option D

  4. Quick Check:

    27 + 23 = 50 and difference = 4 ✅
Hint: Express older as younger + gap, substitute into the sum, solve for younger.
Common Mistakes: Confusing which person is older when setting equations.
5. The combined age of a father and son is 50 years. Father is 30 years older than son. Find their present ages.
medium
A. Father 40, Son 10
B. Father 41, Son 9
C. Father 42, Son 8
D. Father 45, Son 5

Solution

  1. Step 1: Translate to equations.

    Father + Son = 50 and Father = Son + 30.

  2. Step 2: Substitute and solve.

    (Son + 30) + Son = 50 → 2×Son + 30 = 50 → 2×Son = 20 → Son = 10. Father = 10 + 30 = 40.

  3. Final Answer:

    Father = 40, Son = 10 → Option A

  4. Quick Check:

    40 + 10 = 50 and father - son = 30 ✅
Hint: Use substitution for elder = younger + gap, then solve using the sum.
Common Mistakes: Using wrong gap sign or mixing up ages when substituting.

Mock Test

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