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Age/Average Combined Problems

Introduction

Aptitude exams में अक्सर ऐसे questions आते हैं जहाँ ages को average के साथ जोड़ा जाता है। इन problems में group के averages दिए होते हैं और missing ages या totals निकालने होते हैं।

यहां key है: Average Formula = (Sum of Ages ÷ Number of People) इसे age relations के साथ मिलाकर solve किया जाता है।

Pattern: Age/Average Combined Problems

Pattern

Step 1: Average × number of people = total sum of ages.

Step 2: Condition के अनुसार किसी का age जोड़ें या घटाएँ।

Step 3: Missing age या नया average निकालने के लिए equation solve करें।

Step-by-Step Example

Question

5 students की average age 15 years है। एक teacher join करता है और नया average 18 years हो जाता है। Teacher की age निकालें।

Options:

  • A. 28 years
  • B. 30 years
  • C. 33 years
  • D. 36 years

Solution

  1. Step 1: Students का total age निकालें

    Total = 5 × 15 = 75.

  2. Step 2: Teacher आने के बाद total निकालें

    अब 6 लोगों का average = 18 → total = 6 × 18 = 108.

  3. Step 3: Teacher की age निकालें

    Teacher’s age = 108 - 75 = 33.

  4. Final Answer:

    33 years → Option C

  5. Quick Check:

    (75 + 33) ÷ 6 = 108 ÷ 6 = 18 ✅

Quick Variations

Type 1: किसी के join/leave करने पर average बदलता है → missing age find करें।

Type 2: दो groups के अलग-अलग averages दिए हों → combined average या missing group size find करें।

Trick to Always Use

  • Shortcut: New person’s age = (New Average × New Count) - (Old Average × Old Count)
  • Combined groups shortcut: Weighted average = (Sum₁ + Sum₂) ÷ (Count₁ + Count₂)

Summary

Summary

  • Average × Number = Total sum.
  • Join/leave होने पर total sum को adjust करें।
  • Quick Check से हमेशा answer verify करें।

Practice

(1/5)
1. The average age of 4 boys is 12 years. If a new boy joins, the average becomes 13 years. Find the age of the new boy.
easy
A. 16
B. 17
C. 18
D. 19

Solution

  1. Step 1: Compute total age of existing boys

    Total of 4 boys = 4 × 12 = 48.

  2. Step 2: Compute total age after new boy joins

    With 5 boys, total = 5 × 13 = 65.

  3. Step 3: Find the new boy's age

    New boy's age = 65 - 48 = 17.

  4. Final Answer:

    17 → Option B

  5. Quick Check:

    (48 + 17) ÷ 5 = 65 ÷ 5 = 13 ✅
Hint: New age = (new avg × new count) - (old avg × old count).
Common Mistakes: Multiplying averages instead of adjusting sums.
2. The average age of 6 students is 20 years. A teacher of age 32 years joins them. Find the new average age.
easy
A. 21.00
B. 21.71
C. 22.00
D. 22.50

Solution

  1. Step 1: Compute total age of the existing students

    Total age of 6 students = 6 × 20 = 120.

  2. Step 2: Add the teacher’s age

    Add teacher’s age → 120 + 32 = 152.

  3. Step 3: Compute new average

    New average = 152 ÷ 7 = 21.714285... ≈ 21.71.

  4. Final Answer:

    21.71 → Option B

  5. Quick Check:

    21.71 × 7 ≈ 152 → matches total 152 ✅
Hint: New avg = (old total + new entry) ÷ new count.
Common Mistakes: Dividing by old count instead of new count.
3. The average age of 5 people is 25 years. If one person of age 30 years leaves, what is the new average?
medium
A. 22.50
B. 23.75
C. 24.00
D. 24.50

Solution

  1. Step 1: Find the total age of the group

    Total of 5 = 5 × 25 = 125.

  2. Step 2: Subtract the age of the person leaving

    Remove 30 → new total = 95.

  3. Step 3: Compute the new average

    New average = 95 ÷ 4 = 23.75.

  4. Final Answer:

    23.75 → Option B

  5. Quick Check:

    (125 - 30) ÷ 4 = 95 ÷ 4 = 23.75 ✅
Hint: Subtract the leaving person’s age before dividing.
Common Mistakes: Forgetting to reduce the number of people.
4. The average age of 8 students is 21 years. If the age of the teacher is included, the average becomes 22 years. Find the teacher’s age.
medium
A. 28
B. 29
C. 30
D. 31

Solution

  1. Step 1: Compute total age of students

    Total of 8 students = 8 × 21 = 168.

  2. Step 2: Compute total including teacher

    With teacher, 9 people avg = 22 → total = 9 × 22 = 198.

  3. Step 3: Find the teacher’s age

    Teacher’s age = 198 - 168 = 30.

  4. Final Answer:

    30 → Option C

  5. Quick Check:

    (168 + 30) ÷ 9 = 198 ÷ 9 = 22 ✅
Hint: Teacher’s age = (new avg × new count) - old total.
Common Mistakes: Using wrong multiplier for average (22 × 8 instead of 22 × 9).
5. The average age of 10 players is 24 years. If the captain’s age is included, the average increases by 1 year. Find the captain’s age.
hard
A. 30
B. 34
C. 35
D. 36

Solution

  1. Step 1: Compute total age of players

    Total of 10 players = 10 × 24 = 240.

  2. Step 2: Compute new total including the captain

    With captain, 11 people avg = 25 → total = 11 × 25 = 275.

  3. Step 3: Find the captain’s age

    Captain’s age = 275 - 240 = 35.

  4. Final Answer:

    35 → Option C

  5. Quick Check:

    (240 + 35) ÷ 11 = 275 ÷ 11 = 25 ✅
Hint: Person’s age = increase in avg × (n + 1).
Common Mistakes: Forgetting that average increase applies to all members including captain.

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