Quantitative Aptitude
Number System Percentage Profit, Loss & Discount Time & Work Speed, Distance & Time Simple & Compound Interest Ratio, Proportion & Mixture Mensuration Data Interpretation
Module 2 · IBPS PO Quantitative Aptitude

Time & Work

Efficiency, pipes & cisterns, alternate day work, wages.
Efficiency · Pipes & Cisterns · Wages · Alternating Work
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Learning Objectives

  • Understand the fundamental concepts of Time & Work
  • Apply key formulas and techniques to solve problems
  • Practice with exam-level questions to build speed and accuracy

Key Concepts

What is Time & Work?

Time and work problems deal with the relationship between the number of workers, the time taken, and the amount of work done. These questions are a staple in SSC CGL Tier 1 quant and require understanding of work efficiency and the unitary method.

Key Concepts

1. Basic Principle: Work = Rate * Time. If a person completes a job in n days, then their 1-day work = 1/n. Work is often taken as LCM of individual times to simplify calculations.

2. Efficiency: Efficiency is inversely proportional to time. If A takes half the time of B, A is twice as efficient as B. Combined efficiency = sum of individual efficiencies.

3. Pipes & Cisterns: A pipe filling a tank is positive work. A pipe emptying (drain) is negative work. Net work rate = sum of filling rates - sum of emptying rates.

4. Wages: Wages are distributed in proportion to the work done by each person. If A and B work together, their shares are in the ratio of their efficiencies multiplied by their working days.

Solved Examples

Example 1 (Basic)
A can do a job in 12 days and B can do it in 18 days. How long will they take if they work together?

a) 6 days b) 7.2 days c) 7.5 days d) 8 days
Solution: b) 7.2 days. A 1-day work = 1/12. B 1-day work = 1/18. Combined 1-day work = 1/12 + 1/18 = 5/36. Total days = 36/5 = 7.2 days.
Example 2 (Alternate Days)
A can do a job in 10 days and B in 15 days. They work on alternate days starting with A. When will the work be completed?

a) 10 days b) 11 days c) 12 days d) 13 days
Solution: c) 12 days. A 1-day = 1/10 = 3/30, B = 1/15 = 2/30. In 2 days, they do 5/30 = 1/6. In 10 days, they complete 5/6. Remaining 1/6: day 11 A does 3/30, remaining 2/30 done by B on day 12.
Example 3 (Pipes)
Pipe A fills a tank in 8 hours, pipe B fills it in 12 hours, and pipe C drains it in 6 hours. If all three are opened together, how long to fill the tank?

a) 12 hours b) 18 hours c) 24 hours d) 36 hours
Solution: c) 24 hours. A rate = 1/8, B = 1/12, C = -1/6. Net rate = 1/8 + 1/12 - 1/6 = 3/24 + 2/24 - 4/24 = 1/24. Time = 24 hours.

Shortcut Techniques

  • Take LCM of all given times as total work to avoid fractions. If A takes 12 days and B takes 18 days, take work = LCM(12,18) = 36 units. Then A efficiency = 3, B = 2.
  • For "A is thrice as good as B" type, use the ratio of efficiencies directly.
  • For leave/interruption questions, find work done per day and count days accordingly.
  • In pipes & cisterns, if all inlet pipes take a hours and outlet pipes take b hours, net time = 1/(1/a - 1/b).
Pro Tip: Use the LCM method for ALL time and work questions — it eliminates fractions and makes calculations lightning fast. Always check if the work is "remaining work" after some days.

Advanced Applications

Modern exams feature questions combining multiple quantitative concepts. Master these by practicing previous year papers.

Shortcut Methods

Percentages: Use fraction table (12.5%=1/8, 20%=1/5, 25%=1/4). SI/CI: For 2 years, CI-SI = P(r/100)^2. Time Work: Use LCM of time periods. Average Speed: 2ab/(a+b) for equal distances.

Pro Tip
Write key formulas on rough sheet immediately after the exam bell while memory is fresh.

Advanced Applications

Modern exams feature questions combining multiple quantitative concepts. Master these by practicing previous year papers.

Shortcut Methods

Percentages: Use fraction table (12.5%=1/8, 20%=1/5, 25%=1/4). SI/CI: For 2 years, CI-SI = P(r/100)^2. Time Work: Use LCM of time periods. Average Speed: 2ab/(a+b) for equal distances.

Pro Tip
Write key formulas on rough sheet immediately after the exam bell while memory is fresh.

Advanced Applications

Modern exams feature questions combining multiple quantitative concepts. Master these by practicing previous year papers.

Shortcut Methods

Percentages: Use fraction table (12.5%=1/8, 20%=1/5, 25%=1/4). SI/CI: For 2 years, CI-SI = P(r/100)^2. Time Work: Use LCM of time periods. Average Speed: 2ab/(a+b) for equal distances.

Pro Tip
Write key formulas on rough sheet immediately after the exam bell while memory is fresh.

Advanced Applications

Modern exams feature questions combining multiple quantitative concepts. Master these by practicing previous year papers.

Shortcut Methods

Percentages: Use fraction table (12.5%=1/8, 20%=1/5, 25%=1/4). SI/CI: For 2 years, CI-SI = P(r/100)^2. Time Work: Use LCM of time periods. Average Speed: 2ab/(a+b) for equal distances.

Pro Tip
Write key formulas on rough sheet immediately after the exam bell while memory is fresh.

Practice Questions

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