Introduction
Three of the most frequently asked arithmetic topics in Bangladeshi government job exams (BCS, Bank, and IT-officer posts) share one common backbone: the idea of average. Age problems are really disguised average and linear-equation problems, and mixture (alligation) problems are the study of the weighted average of two or more quantities. Master the average and you unlock all three. In almost every preliminary MCQ paper you will find 2–5 marks tied directly to these ideas, and they are fast marks once the method is second nature.
This lesson builds every idea from first principles, gives you clean formulas, the intuition behind them, fully worked exam-style examples, and the shortcuts (like alligation) that turn a two-minute calculation into a ten-second one.
Learning objectives
By the end of this lesson you should be able to:
- Define and compute the arithmetic average (mean) and the weighted average.
- Use the total = average × count relationship fluidly in both directions.
- Solve "a new person joins / leaves and the average changes" problems.
- Handle the classic replacement trick (someone is replaced and the average shifts).
- Set up and solve age problems using a single variable, including ratio-based ages.
- Apply the rule of alligation to mixtures, prices, and concentration/dilution.
- Solve repeated-replacement mixture problems (the milk-and-water drain formula).
- Recognise which method is fastest under exam time pressure.