Average
🔒 Log in to trackOne guaranteed question in almost every Tier 1 shift: a member joining or leaving, a batsman's innings, or a weighted two-group average. The whole topic collapses to one habit — convert averages to sums (Sum = Avg × n) before touching anything.
One page per subtopic: detailed notes, every question type, formulas, tricks and practice sets.
Every formula on one printable page, grouped by subtopic.
5 exam-level questions worked step by step.
60 questions — untimed practice or a timed test with analysis.
Track record in the exam
Questions per shift in recent SSC CGL papers.
Test difficulty mix (60 questions)
Question patterns exams keep repeating
Taken from previous-year papers. If a pattern is marked "very common", expect to see it in your exam.
Someone joins the group
very common"The average age of 30 students is 14. With the teacher, the average goes up by 1."
Turn each average into a total (average × number of people).
The newcomer is the difference of the two totals.
The average age of 30 students is 14 years. When the teacher's age is included, the average rises by 1 year. Find the teacher's age.
Students' total = 30 × 14 = 420
With teacher: 31 people × 15 = 465
Teacher = 465 − 420 = 45 years
One member is replaced (or one wrong entry)
very commonOne person is replaced, or one value was copied wrongly, and the average changes by a known amount.
Total change = number of people × change in average.
Add it to the old person's value (subtract if the average fell).
The average weight of 10 men rises by 1.5 kg when one man weighing 58 kg is replaced by a new man. Find the new man's weight.
Total rise = 10 × 1.5 = 15 kg
New man = old man + rise
58 + 15 = 73 kg
Batsman's average after one more innings
common"Scores 87 in his 17th innings and his average rises by 3."
The new score first lifts the 16 earlier innings by 3 each.
What is left of the score is the new average.
A batsman scores 87 runs in his 17th innings and his average rises by 3. Find his new average.
Lifting 16 earlier innings by 3 = 16 × 3 = 48 runs
New average = 87 − 48 = 39
Check: old average 36, so 16 × 36 + 87 = 663 = 17 × 39
New average = 39
Average of two groups joined
very common"30 boys average 42 kg and 20 girls average 37 kg. Find the class average."
Find each group's total (number × average).
Add the totals and divide by all the people.
30 boys average 42 kg and 20 girls average 37 kg. Find the class average.
Boys: 30 × 42 = 1260
Girls: 20 × 37 = 740
Total = 2000 for 50 students
2000 ÷ 50 = 40 kg
Group sizes from averages
commonBoth group averages and the overall average are given; asks the ratio of the two groups.
Find how far each group's average is from the overall average.
The ratio is those two distances swapped.
The class average is 58; boys average 62 and girls 52. Find boys : girls.
Boys are 62 − 58 = 4 away
Girls are 58 − 52 = 6 away
Swap them: boys : girls = 6 : 4
= 3 : 2
Average of a run of numbers
very common"Average of all multiples of 6 between 1 and 100" or "average of the first n odd numbers".
Evenly spaced numbers: average = (first + last) ÷ 2.
First n counting numbers (1, 2, 3, …): average = (n + 1) ÷ 2.
Find the average of all multiples of 6 between 1 and 100.
Multiples: 6, 12, 18, …, 96 (next is 102, too big)
First + last = 6 + 96 = 102
102 ÷ 2 = 51
Same change to every number
commonAverage and count given with some numbers known, or every number is multiplied or increased by the same amount.
Total = average × count. Subtract the known numbers to find a missing one.
A change done to every number is done to the average too, in the same order.
The average of 6 numbers is 15. Each number is multiplied by 3 and then increased by 5. Find the new average.
Old average = 15
Multiply by 3: 15 × 3 = 45
Add 5: 45 + 5 = 50
Overlapping groups
occasionalTwo parts of one list overlap, e.g. the first 6 and the last 6 of 11 numbers.
Turn every average into a total.
Add the two part totals, then subtract the whole total. What is left is the shared number.
The average of 11 numbers is 50. The first 6 average 49 and the last 6 average 52. Find the 6th number.
First 6: 6 × 49 = 294
Last 6: 6 × 52 = 312
All 11: 11 × 50 = 550
294 + 312 − 550 = 56
Ages in the past or future
common"Five years ago the average age was …" and then a child or new member is added.
Move every age to the same year (each person adds 1 year per year).
Then use totals and adjust the head count.
Five years ago the average age of a husband and wife was 25. Now the average of husband, wife and child is 22. Find the child's age.
Couple 5 years ago: 2 × 25 = 50
Couple now: 50 + 5 + 5 = 60
Family now: 3 × 22 = 66
Child = 66 − 60 = 6 years