Average
π 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 β convert averages to sums (Sum = Avg Γ 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 β 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.
Person joins / leaves, average changes
very commonThe average age, weight or salary of a group is given; a teacher, manager or new member joins (or someone leaves) and the new average is stated.
How to solve: Change both averages into totals and subtract. Shortcut: newcomer = new average + n Γ rise; leaver = new average + n Γ fall. Check with totals.
Example: 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.
Teacher = 15 + 30 Γ 1 = 45 years. (Check: 31 Γ 15 β 30 Γ 14 = 465 β 420 = 45.)
Replacement of one member / wrong entry
very commonOne person is replaced by another, or a value was copied wrongly, and the average changes by a known amount. The count stays the same.
How to solve: Change in total = n Γ change in average, and all of it belongs to the replaced value. For a wrong entry, the average moves by (correct β wrong)/n.
Example: 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.
58 + 10 Γ 1.5 = 73 kg.
Batsman / bowler average
common'Scores x in the nth innings and his average rises by d', or a bowler's runs-per-wicket average improves after a match.
How to solve: Write the old and new totals. Batsman: new average = x β (n β 1)d. Bowler: aW + r = (a β d)(W + w), solve for W.
Example: A batsman scores 87 runs in his 17th innings and his average rises by 3. Find his new average.
87 β 16 Γ 3 = 39. (Old average 36: 16 Γ 36 + 87 = 663 = 17 Γ 39.)
Weighted average of groups
very commonBoys and girls, sections, or workers and managers with separate averages; the combined average or a missing group average is asked.
How to solve: Totals first: combined = Ξ£(n Γ average) Γ· Ξ£n. The answer lies closer to the bigger group. For a missing group, subtract known totals from the overall total.
Example: 30 boys average 42 kg and 20 girls average 37 kg. Find the class average.
(1260 + 740) Γ· 50 = 40 kg.
Group sizes from averages (balance method)
commonBoth group averages and the combined average are given; the ratio or number of members in a group is asked.
How to solve: Sizes are in the reverse ratio of the distances from the combined average: nβ : nβ = (xΜβ β xΜ) : (xΜ β xΜβ). The group closer to the mean is bigger.
Example: The class average is 58; boys average 62 and girls 52. Find boys : girls.
(58 β 52) : (62 β 58) = 6 : 4 = 3 : 2.
Average of standard series and consecutive numbers
very commonAverage of the first n naturals, odd or even numbers, squares, cubes, or of consecutive / equally spaced numbers.
How to solve: Use the table: (n + 1)/2, n, n + 1. Equally spaced numbers: average = middle term = (first + last)/2.
Example: Find the average of all multiples of 6 between 1 and 100.
6, 12, β¦, 96 β (6 + 96)/2 = 51.
Sum bridge and uniform operations
commonAverage and count given with some values known, or every value is increased, multiplied or divided by the same number.
How to solve: Sum = average Γ count, then subtract known values. A uniform operation acts on the average in the same order: Γk then +c gives kA + c.
Example: The average of 6 numbers is 15. Each number is multiplied by 3 and then increased by 5. Find the new average.
15 Γ 3 + 5 = 50.
Overlapping averages and split sets
occasionalAverages over overlapping windows (MonβThu and TueβFri; first 7 and last 7 of 13) or parts of a set with a relation between unknowns.
How to solve: All averages to sums. Overlapping days: subtract and the shared days cancel. First/last parts: shared term = part sums β total. Split set: one variable for the unknown.
Example: The average of 11 numbers is 50. The first 6 average 49 and the last 6 average 52. Find the 6th number.
294 + 312 β 550 = 56.
Ages over time
commonAverage age of a family n years ago or at a marriage / birth, with a child or member added later.
How to solve: Bring every average to the same year: a fixed group's average rises 1 per year. Then use totals and adjust the count.
Example: Five years ago the average age of a husband and wife was 25. Now the average of husband, wife and child is 22. Child's age?
Couple now = 50 + 10 = 60; family = 66 β child = 6 years.