Time and Work – General Aptitude for GATE, PSU, ESE, AE/JE | Priyanka Ma’am

Time and Work is one of the most important topics in General Aptitude and is frequently asked in GATE, PSU, ESE, AE/JE exams. This topic focuses on efficiency, work rate, and time required to complete tasks.

Basic Concept

The fundamental idea is:

Work = Time × Efficiency

Where:

• Work = Total task to be completed
• Time = Time taken to complete the work
• Efficiency = Work done per unit time

Important Formulas

• Efficiency ∝ 1 / Time
• If A can do a work in x days → A’s 1 day work = 1/x
• If A and B work together → Total work per day = (1/x + 1/y)
• Total Time = 1 / (Combined Work Rate)

Key Concepts

1. Individual Work

If a person completes work in x days:

1 day work = 1/x

2. Combined Work

If A takes x days and B takes y days:

1 day work = (1/x + 1/y)

3. Efficiency Ratio

If A is twice as efficient as B:

Efficiency ratio = 2 : 1

Solved Examples

Example 1

A can complete a work in 10 days. What is A’s one day work?

1 day work = 1/10

Example 2

A can do a work in 10 days and B in 20 days. Find time taken together.

1 day work = 1/10 + 1/20 = 3/20
Total time = 20/3 = 6.67 days

Example 3

A is twice as efficient as B. If B takes 12 days, find time taken by A.

Efficiency ratio = 2 : 1
Time ratio = 1 : 2
A takes = 12/2 = 6 days

Example 4 (GATE Level)

A and B together complete work in 8 days. A alone can do it in 12 days. Find B’s time.

A + B = 1/8
A = 1/12
B = (1/8 - 1/12) = (3 - 2)/24 = 1/24
B takes 24 days

Shortcut Tricks

• Use LCM method to simplify fractions
• Assume total work = LCM of given days
• Use efficiency ratio to avoid heavy calculations
• Practice mental calculations for speed

Previous Year Concept Type Questions

Q1. A can do a work in 15 days. B can do it in 10 days. Find time taken together.

1 day work = 1/15 + 1/10 = 1/6
Time = 6 days

Q2. A, B, C can complete work in 6, 8, 12 days respectively. Find combined time.

1 day work = 1/6 + 1/8 + 1/12 = 4/24 + 3/24 + 2/24 = 9/24 = 3/8
Time = 8/3 = 2.67 days

Exam Tips

• Always convert work into fractions
• Use LCM to simplify calculations
• Focus on efficiency instead of time directly
• Practice PYQs for better understanding

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