SSC CGL Quantitative Aptitude: Time and Work

Overview

Time and Work is one of the most important topics in SSC CGL Quantitative Aptitude section. This chapter typically carries 2-3 questions in the exam and is considered scoring if you understand the basic concepts and formulas.

Basic Concepts

1. Work Rate Formula

If a person can complete a work in ‘n’ days, then:

• Work done by the person in 1 day = 1/n
• Time taken to complete the work = 1/(Work rate per day)

2. Combined Work

If A can do a work in ‘a’ days and B can do it in ‘b’ days, then:

• Combined work rate = 1/a + 1/b
• Time taken working together = 1/(1/a + 1/b) = ab/(a+b) days

Important Formulas

1. Basic Formula: Work = Rate × Time
2. Multiple Workers: 1/T = 1/T₁ + 1/T₂ + 1/T₃ + …
3. Efficiency: If A is twice as efficient as B, then A:B = 2:1 in terms of work rate
4. Pipes and Cisterns: Same concept as work problems

Practice Questions

Question 1 (Easy)

A can complete a work in 12 days and B can complete the same work in 18 days. How many days will they take to complete the work together?

Solution:

• A’s work rate = 1/12 per day
• B’s work rate = 1/18 per day
• Combined rate = 1/12 + 1/18 = (3+2)/36 = 5/36 per day
• Time together = 1 ÷ (5/36) = 36/5 = 7.2 days

Answer: 7.2 days

Question 2 (Medium)

A and B together can complete a work in 8 days. A alone can complete it in 12 days. In how many days can B alone complete the work?

Solution:

• Combined rate = 1/8 per day
• A’s rate = 1/12 per day
• B’s rate = 1/8 - 1/12 = (3-2)/24 = 1/24 per day
• B alone can complete in 24 days

Answer: 24 days

Question 3 (Hard)

A can do a piece of work in 10 days, B in 15 days. They work together for 4 days, then A leaves. In how many more days will B complete the remaining work?

Solution:

• A’s rate = 1/10 per day
• B’s rate = 1/15 per day
• Combined rate = 1/10 + 1/15 = (3+2)/30 = 1/6 per day
• Work done in 4 days = 4 × (1/6) = 2/3
• Remaining work = 1 - 2/3 = 1/3
• Time for B to complete 1/3 work = (1/3) ÷ (1/15) = 5 days

Answer: 5 days

Shortcuts and Tips

1. LCM Method

When dealing with multiple workers, use LCM of their individual days:

• If A takes 12 days and B takes 18 days
• LCM(12, 18) = 36
• A’s efficiency = 36/12 = 3 units/day
• B’s efficiency = 36/18 = 2 units/day
• Together = 5 units/day
• Time = 36/5 = 7.2 days

2. Ratio Method

If efficiencies are in ratio, use direct calculation:

• A:B = 3:2 (efficiency ratio)
• If total work = 5 units
• Time together = 5/(3+2) = 1 day for 5 units

3. Percentage Method

Convert work done into percentages for easier calculation.

Common Mistakes to Avoid

1. Confusing efficiency with time: Remember, higher efficiency means less time
2. Adding times instead of rates: Always add work rates, not time periods
3. Forgetting remaining work: Always calculate what fraction of work is left
4. Unit errors: Ensure all calculations are in same time units

Exam Strategy

1. Time Management: Allocate 2-3 minutes per question
2. Formula Sheet: Memorize basic formulas
3. Practice: Solve at least 50 questions of varying difficulty
4. Shortcuts: Use LCM method for faster calculation
5. Verification: Always verify your answer makes logical sense

Previous Year Questions Pattern

• Easy Questions (40%): Basic time and work problems
• Medium Questions (40%): Combined work with variations
• Hard Questions (20%): Complex scenarios with multiple workers

Recommended Practice

1. Solve 10 easy questions daily for concept building
2. Progress to medium level after mastering basics
3. Attempt previous year papers for exam pattern
4. Time yourself to improve speed

This topic is highly scoring in SSC CGL if you practice regularly and understand the underlying concepts. Focus on building speed while maintaining accuracy.