Time and Work

Medium

Time and Work problems relate the rate of work of individuals or groups to the total time taken to complete a task.

Why It Matters

One of the most frequently tested topics in placement aptitude rounds. Questions often involve pipes/cisterns, which are the same concept in a different wrapper.

How It Works

If A can do a job in 'a' days, A's one-day work = 1/a. If A and B work together, combined one-day work = 1/a + 1/b. Total time together = 1 / (1/a + 1/b) = ab / (a + b). LCM method: Take LCM of individual times as total work units. Each person's rate = LCM / their time. This avoids fractions entirely and is faster for competitive exams.

Example

A can do a job in 10 days, B in 15 days. Together: LCM(10,15) = 30 units. A does 3 units/day, B does 2 units/day. Together = 5 units/day. Time = 30/5 = 6 days.

Common Mistakes

The most common error is adding times directly (10 + 15 = 25 days together, or averaging to 12.5 days). You must add RATES, not times.

Test Your Understanding

Easy Q1

A can complete a task in 12 days and B in 18 days. Working together, how many days will they take?

Easy Q2

A can do a job in 10 days. B is 50% more efficient than A. B alone can finish the job in:

Easy Q3

A and B together can do a job in 6 days. A alone takes 10 days. How long does B take alone?

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Related Concepts

Percentage Basics

A percentage expresses a number as a fraction of 100.

Profit and Loss

Profit and loss calculations determine the gain or deficit from a transaction based on cost price and selling price.

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