Banking Notes / Quantitative Aptitude / Chapter 7
Chapter 7 of 26

Average

Simple, weighted, and combined averages — including the age and replacement-based variants banks love to test.

📖 ~8 min read 🏦 Banking Quantitative Aptitude

Introduction

Average = Sum of observations ÷ Number of observations. Banking exams rarely ask a plain average; they wrap it inside replacement, age-group, or combined-average word problems that require careful setup.

Key Formulas

SituationFormula
Combined average of two groups(n₁×A₁ + n₂×A₂) / (n₁+n₂)
Average of first n natural numbers(n+1)/2
Replacement (one member replaced)Change in total = (new average − old average) × total members, adjusted for the replaced value
Average speed (equal distances)2×S1×S2 / (S1+S2)
Q. The average age of 30 students is 12 years. If the teacher's age is included, the average becomes 13 years. Find the teacher's age.
Total age of students = 30×12 = 360. Total with teacher = 31×13 = 403. Teacher's age = 403 − 360 = 43 years.
Q. The average of 8 numbers is 21. If one number is replaced by 35, the average becomes 23. Find the number that was replaced.
Old total = 8×21 = 168. New total = 8×23 = 184. Increase = 184−168 = 16. This increase equals (35 − replaced number), so replaced number = 35 − 16 = 19.
⚠️ Key Insight: For "average speed" over equal distances, never average the two speeds directly — always use the harmonic-mean formula 2×S1×S2/(S1+S2).
💡 Exam Tip: In replacement/inclusion problems, work with totals (Sum = Average × Count) instead of the averages themselves — it converts the problem into simple addition/subtraction.
✅ Practice Focus: Combined average of groups · Inclusion/exclusion of one member · Replacement problems · Average speed for equal distances.

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