Average PDF with Shortcut Tricks, Questions, PYQs, MCQs with Detailed Solutions – Free Download Updated Latest 2025
Average PDF : Are you preparing for SSC, Bank, Railway, UPSC, or other government exams? One of the most scoring topics in the Quantitative Aptitude section is Average. If you’re searching for the best Average PDF that includes shortcut tricks, question-answers, previous year questions (PYQs), and MCQs with detailed solutions, GovernmentAdda.com has you covered — and it’s 100% FREE!
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This FREE PDF includes:
- Concept Explanation of Averages
- Smart & Fast Shortcut Tricks
- Handpicked Previous Year Questions (SSC, IBPS, UPSC)
- 100+ MCQs with Detailed Solutions
- Practice Exercises with Answer Keys
- Chapter-wise Solved Examples
📘 What is Average? — Concept in Simple Words
Average is the arithmetic mean, calculated by summing all values and dividing by the number of values.
🔹 Formula:
Average = (Sum of Observations) / (Number of Observations)
🔹 Example:
If five people have ages: 24, 26, 28, 30, 32
Average = (24 + 26 + 28 + 30 + 32) / 5 = 140 / 5 = 28
✍️ Important Average Formulas to Remember
| Concept | Formula |
|---|---|
| Basic Average | (Sum of Terms) / (Number of Terms) |
| New Average when a value is added | (Old Total + New Value) / (n + 1) |
| Average Speed | 2xy / (x + y) [when distance is same] |
| Weighted Average | (w₁x₁ + w₂x₂ + … + wₙxₙ) / (w₁ + w₂ + … + wₙ) |
| Replacement Formula | New Term = Removed Term ± (Change × Total Terms) |
⚡ Shortcut Tricks to Solve Average Questions Faster
✅ Shortcut 1: Use Deviation from Assumed Average
Choose a nearby number as assumed average. Add or subtract deviations.
Example: Find average of 58, 60, 62, 64, 66
Assumed average = 62
Deviations: -4, -2, 0, +2, +4 = Net = 0
Answer: 62
✅ Shortcut 2: When One Term is Replaced
New term = Replaced term ± (Change in Average × Total Terms)
Example: Average of 10 students increases by 2 when a 40-mark student is replaced. New student’s marks = ?
New student = 40 + (10 × 2) = 60
✅ Shortcut 3: Average of Groups
Use Weighted Average
Average = (n₁×avg₁ + n₂×avg₂ + …) / (n₁ + n₂ + …)
Example:
Class A: 30 students, avg = 70
Class B: 20 students, avg = 80
Overall average = (30×70 + 20×80) / 50 = (2100+1600)/50 = 74
📂 Previous Year Questions (PYQs) on Average – with Solutions
PYQ 1 – SSC CGL 2023
The average of five consecutive odd numbers is 65. What is the largest number?
✅ Solution:
Middle number = 65 → Set = 61, 63, 65, 67, 69
Answer: 69
PYQ 2 – IBPS PO 2022
A batsman scored 200 runs in 5 innings. After the sixth inning, his average increases by 5. What was the score in the sixth inning?
✅ Solution:
Old total = 200, old avg = 40
New avg = 45 → Total after 6 innings = 6 × 45 = 270
Sixth inning = 270 – 200 = 70
PYQ 3 – RRB NTPC 2020
The average of 10 numbers is 50. If one number is 30, what is the average of remaining 9?
✅ Solution:
Total = 10 × 50 = 500
Remaining = 500 – 30 = 470 → Average = 470 / 9 = 52.22
🎯 Top 10 MCQs on Averages with Detailed Solutions
Q1. Find the average of first 10 even numbers.
- A. 10
- B. 11
- C. 12
- D. 9
✅ Answer: B. 11
Explanation: First 10 even numbers = 2, 4, …, 20 → Average = (2 + 20)/2 = 11
Q2. A student scores 80, 85, 90 in three subjects. What is the average?
✅ Answer: (80+85+90)/3 = 255/3 = 85
Q3. Average of 6 numbers is 50. If one more number is added and the new average becomes 52, what is the number added?
✅ Answer:
New total = 52 × 7 = 364
Old total = 50 × 6 = 300
Added number = 364 – 300 = 64
Q4. The average weight of 5 people increases by 2 kg when a new person is added. What is the weight of the new person?
✅ Answer:
New total = 6 × (Old avg + 2) = 6 × (A + 2)
Old total = 5 × A
New person = 6A + 12 – 5A = A + 12
Q5. Find the average of 21, 35, 56, 63, 77
✅ Answer: (21 + 35 + 56 + 63 + 77) / 5 = 252 / 5 = 50.4
🧠 Practice Set for Averages – Free Exercise
Try these questions for practice (solutions included in PDF):
- Average of 6 numbers is 42. One number is 60. Find average of remaining.
- If the average of 10 numbers is 85 and one number is excluded, the average becomes 82. Find the excluded number.
- The average marks of 40 students is 70. If the top 10 students average 90, what is the average of remaining 30?
📥 Download the Full Practice Set with Solutions – Click Here
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📌 Conclusion
The topic of Average is easy to master if practiced regularly with the right methods. The free Average PDF by GovernmentAdda.com is an all-in-one resource containing:
- Time-saving shortcuts
- Chapter-wise theory + formulae
- 100+ MCQs with solutions
- Previous Year Questions from SSC, Bank, UPSC, etc.
📥 Grab your FREE Average PDF now and ace your exams with confidence.
👉 Download Average PDF with Tricks & Questions from GovernmentAdda.com
❓ FAQs – Average PDF by GovernmentAdda
Q1. Is the Average PDF completely free?
✅ Yes, it’s 100% free and downloadable from GovernmentAdda.com.
Q2. Does it include solutions for all questions?
✅ Yes, each MCQ and PYQ comes with a detailed solution.
Q3. Are the shortcut tricks easy to understand?
✅ Absolutely! All tricks are explained with solved examples.
Q4. Is the content updated for 2025 exams?
✅ Yes, the content is aligned with the latest syllabus and trends.
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