What's the best way to master Time and Work Problems quickly?

Master Time and Work Problems by understanding the core concepts first, practicing regularly with our worksheets, and applying the shortcut techniques provided.

Time and Work

Time and Work problems involve calculating the time required for one or more persons to complete a task, given their individual work rates. These problems test your understanding of work rate (work per unit time) and the inverse relationship between time and rate.

10Worksheets

200+Practice Questions

IntermediateDifficulty

3-4 hoursHours to Master

What You'll Learn

Introduction & Overview Why This Matters How to Solve Pro Tips & Tricks

Shortcut Methods Common Mistakes Practice Worksheets Exam Importance

Introduction to Time and Work

Prerequisites

Work rate concept (work/time) Fraction addition/subtraction LCM method Inverse proportionality

Why This Matters: Time and Work problems appear in 2-3 questions in SSC CGL, Banking PO, and Railways exams. They are a staple of quantitative aptitude.

How to Solve Time and Work Problems

Step 1: Let total work = LCM of given times (or 1 unit)

Step 2: Calculate individual work rates: Rate = Total work / Time

Step 3: For combined work: Combined rate = Sum of individual rates

Step 4: Time together = Total work / Combined rate

Step 5: For 'n days alone then together' problems, calculate work done and remaining

Step 6: For efficiency problems, express rates in terms of efficiency

Step 7: Verify that answer is less than individual times

Pro Strategy: Use the LCM method to avoid fractions. Assume total work = LCM of all individual times. This gives integer work rates for easier calculation.

Example Problem

Example: A can complete a work in 10 days, B in 15 days. How many days will they take together? Solution: Step 1: Let total work = LCM(10,15) = 30 units Step 2: A's rate = 30/10 = 3 units/day, B's rate = 30/15 = 2 units/day Step 3: Combined rate = 3 + 2 = 5 units/day Step 4: Time together = 30/5 = 6 days Answer: 6 days Shortcut: 1/10 + 1/15 = (3+2)/30 = 5/30 = 1/6 → 6 days

Pro Tips & Tricks

If A takes a days, B takes b days, together = (a×b)/(a+b) days
If A is p% more efficient than B, then A's rate = B's rate × (1 + p/100)
If A and B together take t days, and A alone takes a days, then B alone = (a×t)/(a-t)
Work done = Rate × Time
Remaining work = 1 - Work done (when total work = 1)
Use unitary method: 1 day's work = 1/Time

Shortcut Methods to Solve Faster

Together time = (a×b)/(a+b) for two persons

For three persons: 1/T = 1/a + 1/b + 1/c

If A takes a days, B takes b days, C takes c days, together = (abc)/(ab+bc+ca)

Common Mistakes to Avoid

Adding times instead of rates

Forgetting to take reciprocal when using 1-day work method

Assuming work rates are additive (they are, but times are not)

Not converting efficiency to rates correctly

Practice Worksheets

Practice makes perfect! Work through these worksheets to master Time and Work. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.

Worksheet 1 Beginner Beginner level - Perfect for building foundational understanding

Worksheet 2 Beginner Beginner level - Perfect for building foundational understanding

Worksheet 3 Beginner Beginner level - Perfect for building foundational understanding

Worksheet 4 Intermediate Intermediate level - Test your understanding with moderate difficulty

Worksheet 5 Intermediate Intermediate level - Test your understanding with moderate difficulty

Worksheet 6 Intermediate Intermediate level - Test your understanding with moderate difficulty

Worksheet 7 Advanced Advanced level - Challenge yourself with complex problems

Worksheet 8 Advanced Advanced level - Challenge yourself with complex problems

Worksheet 9 Advanced Advanced level - Challenge yourself with complex problems

Worksheet 10 Advanced Advanced level - Challenge yourself with complex problems