SSC Time & Work Problems - Complete Guide
SSC Exams

SSC Time & Work Problems - Complete Guide

Welcome to the comprehensive guide on Time & Work problems for SSC exams! This is one of the most important topics in Quantitative Aptitude section and appears frequently in SSC CGL, CHSL, MTS, and other competitive exams.

Understanding Time & Work Basics

Time and Work problems are based on the concept that if a person can complete a work in ‘n’ days, then the person’s one day work = 1/n part of the total work.

Key Formulas You Need to Know

  1. Basic Formula

    • If A can complete a work in ‘a’ days and B can complete the same work in ‘b’ days, then working together they can complete the work in: ab/(a+b) days
  2. Work Rate Formula

    • A’s one day work = 1/a
    • B’s one day work = 1/b
    • Combined work rate = 1/a + 1/b
  3. Time Efficiency Formula

    • If A is ‘n’ times as efficient as B, then:
    • A : B = n : 1 (ratio of work rates)
    • Time ratio = 1 : n (inverse of efficiency ratio)

Types of Time & Work Problems

Type 1: Two People Working Together

Example 1: A can complete a work in 12 days and B can complete the same work in 18 days. In how many days can they complete the work together?

Solution:

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

Type 2: Work and Wages

Example 2: A can do a piece of work in 20 days and B in 30 days. They work together for 4 days, then A leaves. In how many more days will B finish the remaining work?

Solution:

  • Combined work rate = 1/20 + 1/30 = 5/60 = 1/12
  • Work done in 4 days = 4 × 1/12 = 1/3
  • Remaining work = 1 - 1/3 = 2/3
  • Time for B to complete remaining work = (2/3) ÷ (1/30) = 20 days

Important Shortcuts and Tips

Quick Methods:

  1. LCM Method:

    • Assume total work = LCM of individual times
    • Calculate work rates and solve accordingly
  2. Efficiency Method:

    • Compare efficiencies directly
    • Use ratios to solve problems faster
  3. Time Proportions:

    • More efficient person takes less time
    • Time is inversely proportional to efficiency

Practice Questions

Question 1:

A and B together can complete a work in 6 days. A alone can complete it in 10 days. In how many days can B alone complete the work?

Answer: 15 days

Question 2:

12 men can complete a work in 8 days. How many men are required to complete the same work in 6 days?

Answer: 16 men

Question 3:

A is twice as efficient as B. If together they can complete a work in 18 days, find the time taken by A alone.

Answer: 27 days

Common Mistakes to Avoid

  1. Not converting fractions properly - Always find common denominators
  2. Confusing efficiency with time - Remember they are inversely related
  3. Wrong application of formulas - Practice different types thoroughly
  4. Calculation errors - Double-check your arithmetic

Exam Strategy

For SSC Exams:

  • Time allocation: 2-3 minutes per question
  • Difficulty level: Medium to High
  • Expected questions: 2-4 questions in Tier-I
  • Preparation time: 15-20 hours of focused practice
  • Week 1: Learn basic concepts and formulas
  • Week 2: Practice Type 1 & 2 problems
  • Week 3: Advanced problems and shortcuts
  • Week 4: Mock tests and time management

Conclusion

Time & Work is a scoring topic if you master the basic concepts and practice regularly. Focus on understanding the underlying principles rather than memorizing formulas. With consistent practice, you can easily score 100% in this topic.

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