SSC GD Average Notes 2026 – Complete Handwritten Notes, Easy Theory, Formulas & Solved Questions

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Average

SSC GD Maths • Detailed Handwritten Notes • Easy English • Step-by-Step Practice

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📌 Chapter Roadmap

1. Meaning of Average2. Basic Formula3. Change in Average4. Adding a Number5. Removing a Number6. Replacement Questions7. Missing Number8. Consecutive Numbers9. Average of Ages10. Combined Average11. Weighted Average12. Average Speed13. Shortcuts & Exam Traps14. 15 SSC GD Questions15. Final Revision

👉 Main rule: Average × Number = Total. Question ko dekhte hi “total” socho.

1. Meaning of Average

Average tells us the equal share of a total. Suppose five students together have 250 marks. If those 250 marks are shared equally among the five students, each gets 50. That 50 is the average. So average is not a new value; it is a way of representing the whole group with one value.

\[\boxed{\text{Average}=\frac{\text{Sum of all values}}{\text{Number of values}}}\]

✍️ Solved Example 1

Q: Find the average of 18, 24, 30, 36 and 42.

1. First add: \(18+24+30+36+42=150\).
2. There are 5 values.
3. Average \(=150\div5=30\).
4. Answer: \(\boxed{30}\).

✍️ Solved Example 2

Q: The marks of a candidate in 4 tests are 42, 38, 45 and 55. Find the average.

1. Total marks \(=42+38+45+55=180\).
2. Number of tests \(=4\).
3. Average \(=180\div4=45\).
4. Answer: \(\boxed{45}\).

✍️ Solved Example 3

Q: The average of 7 numbers is 16. Find their total.

1. Use the reverse form: Total = Average × Number.
2. Total \(=16\times7=112\).
3. Answer: \(\boxed{112}\).

2. Basic Formula — Three Forms

Most Average questions are built from only three relations. Learn them first. In the exam, identify which quantity is missing and pick the matching form.

\[\boxed{A=\frac{S}{N}}\qquad\boxed{S=A\times N}\qquad\boxed{N=\frac{S}{A}}\]

✍️ Solved Example 1

Q: The average of 12 numbers is 25. Find the sum.

1. Here average \(A=25\), number \(N=12\).
2. So \(S=A\times N=25\times12\).
3. \(S=300\).
4. Answer: \(\boxed{300}\).

✍️ Solved Example 2

Q: The sum of 9 numbers is 252. Find the average.

1. Here \(S=252\) and \(N=9\).
2. \(A=S\div N=252\div9\).
3. \(A=28\).
4. Answer: \(\boxed{28}\).

✍️ Solved Example 3

Q: The sum of some numbers is 360 and their average is 24. How many numbers are there?

1. Use \(N=S/A\).
2. \(N=360\div24=15\).
3. Answer: \(\boxed{15}\) numbers.

3. Change in Average

Whenever one value is added, removed or replaced, do not try to guess the new average. First convert the old average into an old total. Then change the total.

\[\boxed{\text{Old Total}=\text{Old Average}\times\text{Old Number}}\]

✍️ Solved Example 1

Q: Average of 5 numbers is 24. A new number 36 is added. Find the new average.

1. Old total \(=24\times5=120\).
2. New total \(=120+36=156\).
3. New number of values \(=6\).
4. New average \(=156\div6=26\).
5. Answer: \(\boxed{26}\).

✍️ Solved Example 2

Q: Average of 8 numbers is 31. One number 24 is removed. Find the new average.

1. Old total \(=31\times8=248\).
2. New total \(=248-24=224\).
3. New count \(=7\).
4. New average \(=224\div7=32\).
5. Answer: \(\boxed{32}\).

✍️ Solved Example 3

Q: Average of 6 numbers is 18. A number 12 is replaced by 30. Find the new average.

1. Old total \(=18\times6=108\).
2. Change in total \(=30-12=18\).
3. New total \(=126\).
4. Count remains 6.
5. New average \(=126\div6=21\).
6. Answer: \(\boxed{21}\).

4. Adding a Number

When a new value joins the group, two things change: total increases and count also increases by 1. This is the point many students miss.

\[\boxed{\text{New Average}=\frac{\text{Old Average}\times N+\text{New Value}}{N+1}}\]

✍️ Solved Example 1

Q: Average of 10 numbers is 22. If 32 is added, find the new average.

1. Old total \(=22\times10=220\).
2. New total \(=220+32=252\).
3. New count \(=11\).
4. New average \(=252\div11=22\frac{10}{11}\).
5. Answer: \(\boxed{22\frac{10}{11}}\).

✍️ Solved Example 2

Q: Average of 7 students is 40 marks. A new student scores 54. Find the new average.

1. Old total \(=40\times7=280\).
2. New total \(=280+54=334\).
3. New count \(=8\).
4. New average \(=334\div8=41.75\).
5. Answer: \(\boxed{41.75}\) marks.

✍️ Solved Example 3

Q: Average of 12 values is 28. A value 16 is added. Find the new average.

1. Old total \(=28\times12=336\).
2. New total \(=336+16=352\).
3. New count \(=13\).
4. New average \(=352\div13=27\frac{1}{13}\).
5. Answer: \(\boxed{27\frac{1}{13}}\).

5. Removing a Number

When one value leaves the group, subtract it from the old total and reduce the count by 1. Keep the old and new counts separate.

\[\boxed{\text{New Average}=\frac{\text{Old Average}\times N-\text{Removed Value}}{N-1}}\]

✍️ Solved Example 1

Q: Average of 9 numbers is 26. One number 18 is removed. Find the new average.

1. Old total \(=26\times9=234\).
2. New total \(=234-18=216\).
3. New count \(=8\).
4. New average \(=216\div8=27\).
5. Answer: \(\boxed{27}\).

✍️ Solved Example 2

Q: Average of 6 numbers is 35. One value 20 is removed. Find the new average.

1. Old total \(=35\times6=210\).
2. New total \(=210-20=190\).
3. New count \(=5\).
4. New average \(=190\div5=38\).
5. Answer: \(\boxed{38}\).

✍️ Solved Example 3

Q: Average of 10 ages is 24 years. A person aged 15 leaves. Find the new average.

1. Old total age \(=24\times10=240\).
2. New total \(=240-15=225\).
3. New count \(=9\).
4. New average \(=225\div9=25\).
5. Answer: \(\boxed{25}\) years.

6. Replacement of a Number

Replacement is different from addition or removal because the number of items does not change. The safest way is to find the difference between new and old value and adjust the old total.

\[\boxed{\text{New Average}=\text{Old Average}+\frac{\text{New Value}-\text{Old Value}}{N}}\]

✍️ Solved Example 1

Q: Average of 8 numbers is 25. If 18 is replaced by 34, find the new average.

1. Old total \(=25\times8=200\).
2. Increase \(=34-18=16\).
3. New total \(=216\).
4. Count stays 8.
5. New average \(=216\div8=27\).
6. Answer: \(\boxed{27}\).

✍️ Solved Example 2

Q: Average of 12 numbers is 30. If 44 is replaced by 20, find the new average.

1. Old total \(=30\times12=360\).
2. Change \(=20-44=-24\).
3. New total \(=360-24=336\).
4. Count remains 12.
5. New average \(=336\div12=28\).
6. Answer: \(\boxed{28}\).

✍️ Solved Example 3

Q: Average of 5 values is 18. One value 9 is replaced by 24. Find the new average.

1. Old total \(=18\times5=90\).
2. Increase \(=24-9=15\).
3. New total \(=105\).
4. Count remains 5.
5. New average \(=105\div5=21\).
6. Answer: \(\boxed{21}\).

7. Missing Number from Average

If the average and all but one value are known, first calculate the required total, then subtract the known values. This turns an apparently difficult question into simple arithmetic.

\[\boxed{\text{Missing Value}=\text{Required Total}-\text{Sum of Known Values}}\]

✍️ Solved Example 1

Q: The average of 5 numbers is 32. Four numbers are 28, 35, 30 and 41. Find the fifth number.

1. Required total \(=32\times5=160\).
2. Known sum \(=28+35+30+41=134\).
3. Missing value \(=160-134=26\).
4. Answer: \(\boxed{26}\).

✍️ Solved Example 2

Q: Average marks of 6 tests is 45. Five scores are 42, 48, 39, 50 and 44. Find the missing score.

1. Required total \(=45\times6=270\).
2. Known total \(=42+48+39+50+44=223\).
3. Missing score \(=270-223=47\).
4. Answer: \(\boxed{47}\).

✍️ Solved Example 3

Q: Average of 8 numbers is 27. Seven numbers total 175. Find the eighth number.

1. Required total \(=27\times8=216\).
2. Seven-number sum \(=175\).
3. Missing number \(=216-175=41\).
4. Answer: \(\boxed{41}\).

8. Average of Consecutive / Equally Spaced Numbers

For numbers with equal gaps, the average lies exactly at the centre. For an odd number of such terms, the middle term itself is the average. This is a great time-saving idea.

\[\boxed{\text{Average}=\frac{\text{First term}+\text{Last term}}{2}}\]

✍️ Solved Example 1

Q: Find the average of 11, 13, 15, 17 and 19.

1. First term = 11, last term = 19.
2. Average \(=(11+19)\div2=30\div2\).
3. Average \(=15\).
4. Answer: \(\boxed{15}\).

✍️ Solved Example 2

Q: The average of five consecutive integers is 42. Find the integers.

1. For five consecutive integers, the middle number equals the average.
2. Middle number = 42.
3. So the numbers are \(40,41,42,43,44\).
4. Answer: \(\boxed{40,41,42,43,44}\).

✍️ Solved Example 3

Q: Find the average of 24, 29, 34, 39 and 44.

1. The numbers have equal gap 5.
2. Use centre formula: \((24+44)\div2=68\div2\).
3. Average \(=34\).
4. Answer: \(\boxed{34}\).

9. Average of Ages

Age questions are ordinary average questions written in story form. Convert the given average into total age, then add or subtract the required age.

\[\boxed{\text{Total Age}=\text{Average Age}\times\text{Number of Persons}}\]

✍️ Solved Example 1

Q: Average age of 5 friends is 22 years. Find their total age.

1. Total age \(=22\times5=110\).
2. Answer: \(\boxed{110}\) years.

✍️ Solved Example 2

Q: Average age of 6 persons is 24 years. A new person aged 36 joins. Find the new average.

1. Old total \(=24\times6=144\).
2. New total \(=144+36=180\).
3. New count \(=7\).
4. New average \(=180\div7=25\frac{5}{7}\).
5. Answer: \(\boxed{25\frac{5}{7}}\) years.

✍️ Solved Example 3

Q: Average age of 8 persons is 27 years. One person aged 20 leaves. Find the new average.

1. Old total \(=27\times8=216\).
2. New total \(=216-20=196\).
3. New count \(=7\).
4. New average \(=196\div7=28\).
5. Answer: \(\boxed{28}\) years.

10. Combined Average

For two groups, do not average the two average values directly unless both groups contain the same number of items. First calculate each group's total.

\[\boxed{\text{Combined Average}=\frac{n_1a_1+n_2a_2}{n_1+n_2}}\]

✍️ Solved Example 1

Q: 20 students have an average of 45 marks and 30 students have an average of 55 marks. Find the combined average.

1. First group total \(=20\times45=900\).
2. Second group total \(=30\times55=1650\).
3. Combined total \(=2550\).
4. Total students \(=50\).
5. Combined average \(=2550\div50=51\).
6. Answer: \(\boxed{51}\).

✍️ Solved Example 2

Q: 12 workers earn an average of ₹18,000 and 8 workers earn an average of ₹15,000. Find the combined average salary.

1. First total \(=12\times18,000=216,000\).
2. Second total \(=8\times15,000=120,000\).
3. Combined total \(=336,000\).
4. Total workers \(=20\).
5. Combined average \(=336,000\div20=16,800\).
6. Answer: \(\boxed{₹16,800}\).

✍️ Solved Example 3

Q: Group A has 25 students with average 32 marks. Group B has 15 students with average 44 marks. Find the combined average.

1. A total \(=25\times32=800\).
2. B total \(=15\times44=660\).
3. Combined total \(=1460\).
4. Total students \(=40\).
5. Average \(=1460\div40=36.5\).
6. Answer: \(\boxed{36.5}\).

11. Weighted Average — Easy Understanding

A larger group must influence the combined average more than a smaller group. That is why simply taking the mean of two different-sized group averages can give the wrong answer.

\[\boxed{\text{Weighted Average}=\frac{w_1x_1+w_2x_2+\cdots}{w_1+w_2+\cdots}}\]

✍️ Solved Example 1

Q: 3 students score 60 and 7 students score 80. Find the average score.

1. Total score \(=3\times60+7\times80=180+560=740\).
2. Total students \(=10\).
3. Average \(=740\div10=74\).
4. Answer: \(\boxed{74}\).

✍️ Solved Example 2

Q: 4 kg rice costs ₹40/kg and 6 kg costs ₹50/kg. Find the average cost per kg.

1. Total cost \(=4\times40+6\times50=160+300=460\).
2. Total quantity \(=10\) kg.
3. Average cost \(=460\div10=46\).
4. Answer: \(\boxed{₹46/kg}\).

✍️ Solved Example 3

Q: 5 students have average 42 marks and 15 students have average 54 marks. Find the combined average.

1. First total \(=5\times42=210\).
2. Second total \(=15\times54=810\).
3. Combined total \(=1020\).
4. Total students \(=20\).
5. Average \(=1020\div20=51\).
6. Answer: \(\boxed{51}\).

12. Average Speed

Average speed is distance divided by total time. The common trap is to take the simple average of two speeds without checking the journey conditions.

\[\boxed{\text{Average Speed}=\frac{\text{Total Distance}}{\text{Total Time}}}\]

✍️ Solved Example 1

Q: A car covers 150 km in 3 hours. Find its average speed.

1. Average speed \(=150\div3=50\).
2. Answer: \(\boxed{50}\) km/h.

✍️ Solved Example 2

Q: A vehicle travels 60 km in 2 hours and 90 km in 3 hours. Find average speed.

1. Total distance \(=60+90=150\) km.
2. Total time \(=2+3=5\) hours.
3. Average speed \(=150\div5=30\) km/h.
4. Answer: \(\boxed{30}\) km/h.

✍️ Solved Example 3

Q: A person travels 24 km at 6 km/h. Find the travel time.

1. Time \(=Distance\div Speed=24\div6\).
2. Time \(=4\) hours.
3. Answer: \(\boxed{4}\) hours.

13. Shortcuts, Margin Notes & Exam Traps

⚡ Shortcut 1: If every number increases by 5, average also increases by 5. If every number decreases by 3, average decreases by 3.

⚡ Shortcut 2: For consecutive/equally spaced numbers, average = (first + last) ÷ 2.

⚡ Shortcut 3: In replacement, only the difference matters: New Average = Old Average + (New − Old) ÷ Number.

⚠️ Common Exam Traps

• Adding a new value but forgetting to increase the number of values.
• Removing a value but still dividing by the old count.
• For replacement, changing the count even though no item was added or removed.
• Taking the average of two group averages when the group sizes are different.
• Taking a simple average of speeds instead of total distance ÷ total time.

✍️ Think like a student: “First total, then count, then divide.” This one line solves a very large part of Average chapter.

14. 15 Fully Solved SSC GD Practice Questions

Q1. Find average of 25, 30, 35, 40, 45.

1. Sum \(=175\).
2. Count \(=5\).
3. Average \(=175\div5=35\).
4. Answer: \(\boxed{35}\).

Q2. Average of 15 numbers is 24. Find total.

1. Total \(=15\times24=360\).
2. Answer: \(\boxed{360}\).

Q3. Sum of 12 numbers is 420. Find average.

1. Average \(=420\div12=35\).
2. Answer: \(\boxed{35}\).

Q4. Average of 6 numbers is 28. If 40 is added, find the new average.

1. Old total \(=28\times6=168\).
2. New total \(=208\).
3. New count \(=7\).
4. Average \(=208\div7=29\frac{5}{7}\).
5. Answer: \(\boxed{29\frac{5}{7}}\).

Q5. Average of 7 numbers is 31. If 17 is removed, find new average.

1. Old total \(=31\times7=217\).
2. New total \(=200\).
3. New count \(=6\).
4. Average \(=200\div6=33\frac{1}{3}\).
5. Answer: \(\boxed{33\frac{1}{3}}\).

Q6. Average of 10 numbers is 26. Replace 14 by 34.

1. Old total \(=260\).
2. Increase \(=20\).
3. New total \(=280\).
4. Average \(=280\div10=28\).
5. Answer: \(\boxed{28}\).

Q7. Average of 5 numbers is 22. Four numbers sum to 78. Find the fifth number.

1. Required total \(=22\times5=110\).
2. Missing value \(=110-78=32\).
3. Answer: \(\boxed{32}\).

Q8. Find average of first 9 odd numbers.

1. First 9 odd numbers are equally spaced from 1 to 17.
2. Average \(=(1+17)\div2=9\).
3. Answer: \(\boxed{9}\).

Q9. Average age of 8 persons is 25. A person aged 33 joins. Find new average.

1. Old total \(=25\times8=200\).
2. New total \(=233\).
3. New count \(=9\).
4. Average \(=233\div9=25\frac{8}{9}\).
5. Answer: \(\boxed{25\frac{8}{9}}\).

Q10. 18 students average 42 and 12 students average 57. Find combined average.

1. First total \(=18\times42=756\).
2. Second total \(=12\times57=684\).
3. Combined total \(=1440\).
4. Total students \(=30\).
5. Average \(=48\).
6. Answer: \(\boxed{48}\).

Q11. A bus covers 240 km in 6 hours. Find average speed.

1. Average speed \(=240\div6=40\).
2. Answer: \(\boxed{40}\) km/h.

Q12. Average of 9 values is 18. Each value is increased by 4. Find the new average.

1. Every value rises by 4.
2. So average also rises by 4.
3. New average \(=18+4=22\).
4. Answer: \(\boxed{22}\).

Q13. Average of 12 values is 20. Each value is reduced by 3. Find the new average.

1. Every value falls by 3.
2. New average \(=20-3=17\).
3. Answer: \(\boxed{17}\).

Q14. 6 items have value 15 and 4 items have value 25. Find average.

1. Total \(=6\times15+4\times25=90+100=190\).
2. Total items \(=10\).
3. Average \(=190\div10=19\).
4. Answer: \(\boxed{19}\).

Q15. A person's average speed for a journey is 45 km/h and total time is 8 hours. Find total distance.

1. Distance \(=Speed\times Time=45\times8=360\) km.
2. Answer: \(\boxed{360}\) km.

15. Final Revision — One Minute Before Exam

Must Remember

\[\boxed{A=\frac{S}{N}}\quad\boxed{S=A\times N}\quad\boxed{N=\frac{S}{A}}\]

• ✓ Average = equal representation of the total.
• ✓ Added value → total increases and count increases by 1.
• ✓ Removed value → total decreases and count decreases by 1.
• ✓ Replaced value → count stays same; change the total by New − Old.
• ✓ Missing value = required total − known total.
• ✓ Equally spaced numbers → average = (first + last) ÷ 2.
• ✓ Combined average → combine totals, not just averages.
• ✓ Average speed = total distance ÷ total time.

Final self-check: Before marking the answer, ask: “Did I use the correct count?” This single check prevents many Average mistakes.

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SSC GD Maths • Average Notes 2026

Human-style notebook format • Detailed theory • Step-by-step solutions • Exam shortcuts