Introduction
Time and Work problems ask how long a job takes when one or more people (or machines, pipes, taps) work on it — alone or together, sometimes at different speeds. This is one of the highest-frequency arithmetic topics in Bangladeshi government job exams (BCS Preliminary, Bank, and IT-officer MCQ and written papers). A handful of stable ideas — mainly the concept of work rate — lets you solve almost every question in under a minute, often without a calculator. Master this chapter and you convert several "hard-looking" marks into guaranteed marks.
The single most important idea is simple: if a person finishes a job in n days, then in one day they finish 1/n of the job. Everything else in this lesson is built from that one sentence.
Learning Objectives
- Understand work as a quantity and rate as work done per unit time.
- Convert "finishes in n days" into a per-day rate 1/n and back.
- Add and subtract rates to handle people working together, leaving, or joining.
- Solve combined-work, wage-sharing, and partial-work problems.
- Handle the pipes and cisterns variant (filling and emptying) as a signed-rate problem.
- Use the fast LCM units-of-work method to avoid fractions entirely.
- Apply efficiency ratios (man/woman/boy, "twice as fast") and the man-days formula.
- Avoid the classic traps examiners deliberately set.