Time and Work - Aptitude Questions & Answers
Time and Work is one of the most important topics in Quantitative Aptitude. In this lesson, you will learn concepts, formulas, shortcuts, solved examples, and aptitude questions with answers. This topic is useful for exams like SSC, Bank, CAT, TCS, and other competitive exams.
Master time and work problems with this comprehensive guide covering efficiency concepts, pipe calculations, and wage distribution. Learn essential formulas and shortcut methods to solve aptitude questions quickly and accurately for competitive exams.
Time and Work: Complete Guide with Formulas & Shortcut Methods
Core Concepts of Time and Work
Time
Duration taken to complete a particular task or work. Usually measured in days, hours, or minutes.
Efficiency
Work done per unit time. Efficiency is inversely proportional to the time taken to complete work.
Work
Product of time and efficiency. Represents the total task or job to be completed.
Important Note
If a piece of work is done in x number of days, then the work done in one day = 1/x
Essential Rules and Tricks for Time and Work
Rule 1: Two Persons Working Together
If A can do a task in x days, and B can do it in y days, working together they complete the task in:
Method 1: Direct Formula
Method 2: LCM Method (Recommended)
- Assume total work = LCM(x, y)
- Efficiency of A = LCM/x
- Efficiency of B = LCM/y
- Combined efficiency = (LCM/x) + (LCM/y)
- Time = Total work ÷ Combined efficiency
Example: Aman can do a task in 8 days and Ajeet can do it in 12 days. How many days if they work together?
Solution using LCM Method:
- Total work = LCM(8, 12) = 24 units
- Aman\'s efficiency = 24/8 = 3 units/day
- Ajeet\'s efficiency = 24/12 = 2 units/day
- Combined efficiency = 3 + 2 = 5 units/day
- Time = 24 ÷ 5 = 4.8 days or 24/5 days
Rule 2: Three Persons Working Together
If A, B, and C can do a task in x, y, and z days respectively, working together they complete the task in:
LCM Method:
- Assume total work = LCM(x, y, z)
- Efficiency of A = LCM/x
- Efficiency of B = LCM/y
- Efficiency of C = LCM/z
- Combined efficiency = Sum of all efficiencies
- Time = Total work ÷ Combined efficiency
Example: A can do a task in 2 days, B in 3 days, and C in 6 days. How many days if all work together?
Solution:
- Total work = LCM(2, 3, 6) = 6 units
- A\'s efficiency = 6/2 = 3 units/day
- B\'s efficiency = 6/3 = 2 units/day
- C\'s efficiency = 6/6 = 1 unit/day
- Combined efficiency = 3 + 2 + 1 = 6 units/day
- Time = 6 ÷ 6 = 1 day
Pipes and Cisterns: Filling and Emptying Problems
Basic Definitions
Inlet Pipe
A pipe that fills the tank or cistern. Positive work.
Outlet Pipe
A pipe that empties the tank or cistern. Negative work.
Important Note
If pipe A fills a tank in x hours, then the part of tank filled in one hour = 1/x
Rule 1: Two Inlet Pipes
If pipe A fills a tank in x hours and pipe B fills it in y hours, together they fill the tank in:
Direct Formula:
Example: Pipe A fills a cistern in 40 hours, Pipe B in 60 hours. How long if both are opened together?
Solution using LCM Method:
- Total capacity = LCM(40, 60) = 120 liters
- Pipe A efficiency = 120/40 = 3 L/hour
- Pipe B efficiency = 120/60 = 2 L/hour
- Combined efficiency = 3 + 2 = 5 L/hour
- Time = 120 ÷ 5 = 24 hours
Rule 2: Inlet and Outlet Pipes Together
If inlet pipes A and B fill in x and y hours, and outlet pipe C empties in z hours:
LCM Method with Negative Efficiency:
- Assume total capacity = LCM(x, y, z)
- Efficiency of A = LCM/x (positive)
- Efficiency of B = LCM/y (positive)
- Efficiency of C = -LCM/z (negative)
- Net efficiency = Sum of all efficiencies
- Time = Total capacity ÷ Net efficiency
Example: Pipes A and B fill a tank in 12 and 18 hours. Pipe C empties it in 30 hours. All opened together?
Solution:
- Total capacity = LCM(12, 18, 30) = 180 liters
- A\'s efficiency = 180/12 = 15 L/hour
- B\'s efficiency = 180/18 = 10 L/hour
- C\'s efficiency = -180/30 = -6 L/hour
- Net efficiency = 15 + 10 - 6 = 19 L/hour
- Time = 180 ÷ 19 = 180/19 hours ≈ 9.47 hours
Man-Chain-Rule and Work Distribution
Man-Chain-Rule Formula
Where:
- M = Number of workers
- D = Number of days
- H = Working hours per day
- E = Efficiency ratio
- W = Units of work
Basic Concept
If a worker completes 1/x work in one day, total work takes x days.
Example: Akhil completes ⅓ of work daily. Total days = 1 ÷ (⅓) = 3 days
Example 1: 18 men take 15 days to complete a task. How many days for 45 men?
Solution using M₁D₁ = M₂D₂ (when work is same):
D₂ = (18 × 15) ÷ 45 = 6 days
Example 2: 16 workers complete a project in 18 days, 10 technicians finish in 10 days. Find worker:technician capacity ratio.
Solution:
- 1 worker\'s 1 day work = 1/(16 × 18) = 1/288
- 1 technician\'s 1 day work = 1/(10 × 10) = 1/100
- Ratio = (1/288) : (1/100) = 100:288 = 25:72
Wage Distribution Based on Work
Wage Calculation Principle
Wages are distributed in proportion to work done or efficiency. If persons work together, wages are divided according to their contribution.
Formula:
Wage ∝ Work done ∝ Efficiency × Time
Example: X and Y together earn ₹500 for 1 day\'s work. X earns ₹800 for 4 days work. How much does Y earn in 10 days?
Step-by-Step Solution:
- X + Y per day = ₹500
- X\'s 4 days = ₹800 → X\'s per day = 800 ÷ 4 = ₹200
- Y\'s per day = (X + Y) - X = 500 - 200 = ₹300
- Y\'s 10 days = 10 × 300 = ₹3,000
Frequently Asked Questions
What is the best method to solve time and work problems?
The LCM method is most recommended as it avoids fractions and provides a clear visual approach. Assume total work as LCM of individual times.
How to handle negative work in pipes and cisterns?
Treat outlet pipes as negative efficiency. Add all efficiencies (positive for inlets, negative for outlets) to get net efficiency.
What if workers have different efficiencies?
Use efficiency ratios in the man-chain-rule formula: (M × D × H × E)/W remains constant for same work.
How to divide wages fairly among workers?
Wages should be proportional to work done. Calculate each person\'s contribution (efficiency × time) and divide total wages accordingly.
Can the LCM method be used for more than 3 persons?
Yes! The LCM method works for any number of workers/pipes. Just find LCM of all time values and calculate individual efficiencies.
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Frequently Asked Questions
What is Time and Work?
Time and Work is an important aptitude topic used in competitive exams that tests your logical reasoning and problem-solving abilities.
Is Time and Work important for competitive exams?
Yes, Time and Work is frequently asked in SSC, Bank, CAT, TCS, and other placement exams. It's essential to master this topic for better scores.
How to prepare Time and Work easily?
Practice solved examples, learn formulas and shortcuts, and attempt practice questions regularly to master Time and Work.
What are the important formulas in Time and Work?
Key formulas vary by topic, but generally include basic concepts, shortcuts, and standard problem-solving approaches specific to Time and Work.
How many questions come from Time and Work?
Typically 5-10 questions come from Time and Work in most competitive exams, making it a high-scoring section.
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