Time and Work - Mathematics (SSC CGL CHSL)

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Introduction to Time and Work Work Done by Multiple People
Work Done by One Person

In this part, we’ll apply the concepts introduced earlier to real scenarios where a single person is doing the work. These are typically the most basic yet crucial types of problems in Time and Work.

1. Basic Idea Recap

If a person completes a work in x days, then the work done in one day is:

\[ \text{One day’s work} = \frac{1}{x} \]

If the person works for n days, then the total work done is:

\[ \text{Total work done in } n \text{ days} = n \times \frac{1}{x} = \frac{n}{x} \]

And if the person has completed \( \frac{n}{x} \) part of the work, then the remaining work is:

\[ 1 - \frac{n}{x} \]

Let us now understand this through step-by-step examples.

2. Example 1: Finding Work Done in Some Days

Question: A person can complete a work in 20 days. How much work will they do in 7 days?

Step 1: One day’s work = \( \frac{1}{20} \)

Step 2: In 7 days, work done =

\[ 7 \times \frac{1}{20} = \frac{7}{20} \]

Answer: \( \frac{7}{20} \) of the work is completed.

3. Example 2: Finding Days to Complete Work

Question: A person completes \( \frac{3}{5} \) of a work in 6 days. How many total days are needed to complete the whole work?

Step 1: Work done in 6 days = \( \frac{3}{5} \)

Step 2: Work done in 1 day =

\[ \frac{3}{5} \div 6 = \frac{3}{5 \times 6} = \frac{1}{10} \]

Step 3: Total time to complete full work =

\[ 1 \div \frac{1}{10} = 10 \text{ days} \]

Answer: The full work will be completed in 10 days.

4. Example 3: Finding Remaining Work

Question: A completes a work in 15 days. How much work is left after he has worked for 4 days?

Step 1: One day’s work = \( \frac{1}{15} \)

Step 2: Work done in 4 days =

\[ 4 \times \frac{1}{15} = \frac{4}{15} \]

Step 3: Remaining work =

\[ 1 - \frac{4}{15} = \frac{11}{15} \]

Answer: \( \frac{11}{15} \) of the work remains.

5. Practice Tips

  • Always convert days to one-day work before solving.
  • Use fractions to represent parts of work done or remaining.
  • Be comfortable with multiplying and dividing fractions.

In the next part, we’ll move on to a slightly more complex but very common situation — when two or more people work together to complete a task. We'll also learn how to use the LCM method to handle such problems more efficiently.