All Exams Quantitative Aptitude: Time & Work — Complete Concept Guide with MCQs

Exam: All Exams | Subject: Quantitative Aptitude | Topic: Time & Work | Year: 2026

Concept Overview

Time and Work is a consistently high-scoring topic in SSC exams. Problems involve workers completing tasks alone or together, pipes filling/emptying tanks, and efficiency comparisons. Master the unit approach for quick solutions.

Core Concepts

  • Basic Formula: If A completes work in 'n' days → A's 1-day work = 1/n
  • Combined Work: (A+B)'s 1-day work = 1/A + 1/B → Time = AB/(A+B)
  • Efficiency Ratio: If A is k times as efficient as B, and together they take T days → B alone takes T(k+1) days
  • Work and Wages: Wages are distributed in ratio of work done (= ratio of 1-day work × days worked)
  • Pipes & Cisterns: Inlet pipe: +ve work rate; Outlet pipe: -ve work rate
⚡ LCM Method: Assume total work = LCM of individual days. Then find each person's daily work as whole numbers. Avoids fractions completely! Example: A=12 days, B=18 days → Work = LCM(12,18) = 36 units. A does 3 units/day, B does 2 units/day. Together: 5 units/day → 36/5 = 7.2 days.

Practice MCQs (10 Questions)

Test your understanding of Time & Work with these All Exams level questions.

Q1. A can complete work in 12 days, B in 18 days. Together they complete in:

  1. 7.2 days
  2. 8 days
  3. 6 days
  4. 9 days

Explanation: A's 1-day work = 1/12, B's = 1/18. Together = 1/12 + 1/18 = 3/36 + 2/36 = 5/36. Time = 36/5 = 7.2 days.

Q2. A does 2/3 of work in 10 days. Time to complete rest:

  1. 5 days
  2. 4 days
  3. 6 days
  4. 3 days

Explanation: 2/3 of work → 10 days. Full work → 15 days. Remaining = 1/3 of work → 15 × 1/3 = 5 days.

Q3. A is twice as efficient as B. Together they finish in 14 days. B alone takes:

  1. 42 days
  2. 28 days
  3. 21 days
  4. 56 days

Explanation: A = 2B in efficiency. (A+B) = 3B. 3B does work in 14 days. B alone = 14 × 3 = 42 days.

Q4. A and B can finish a work in 30 days. B and C in 40 days, A and C in 60 days. Together:

  1. 960/47 ≈ 20.4 days
  2. 25 days
  3. 20 days
  4. 24 days

Explanation: 2(A+B+C) = 1/30+1/40+1/60 = 4/120+3/120+2/120 = 9/120 = 3/40. A+B+C = 3/80. Time = 80/3 ≈ 26.67 days. (Standard formula approach)

Q5. A tap fills a tank in 6 hours, another empties in 9 hours. Net fill time (both open):

  1. 18 hours
  2. 15 hours
  3. 12 hours
  4. 27 hours

Explanation: Net rate = 1/6 - 1/9 = 3/18 - 2/18 = 1/18 per hour. Tank fills in 18 hours.

Q6. A can complete work in 12 days, B in 18 days. Together they complete in:

  1. 7.2 days
  2. 8 days
  3. 6 days
  4. 9 days

Explanation: A's 1-day work = 1/12, B's = 1/18. Together = 1/12 + 1/18 = 3/36 + 2/36 = 5/36. Time = 36/5 = 7.2 days.

Q7. A does 2/3 of work in 10 days. Time to complete rest:

  1. 5 days
  2. 4 days
  3. 6 days
  4. 3 days

Explanation: 2/3 of work → 10 days. Full work → 15 days. Remaining = 1/3 of work → 15 × 1/3 = 5 days.

Q8. A is twice as efficient as B. Together they finish in 14 days. B alone takes:

  1. 42 days
  2. 28 days
  3. 21 days
  4. 56 days

Explanation: A = 2B in efficiency. (A+B) = 3B. 3B does work in 14 days. B alone = 14 × 3 = 42 days.

Q9. A and B can finish a work in 30 days. B and C in 40 days, A and C in 60 days. Together:

  1. 960/47 ≈ 20.4 days
  2. 25 days
  3. 20 days
  4. 24 days

Explanation: 2(A+B+C) = 1/30+1/40+1/60 = 4/120+3/120+2/120 = 9/120 = 3/40. A+B+C = 3/80. Time = 80/3 ≈ 26.67 days. (Standard formula approach)

Q10. A tap fills a tank in 6 hours, another empties in 9 hours. Net fill time (both open):

  1. 18 hours
  2. 15 hours
  3. 12 hours
  4. 27 hours

Explanation: Net rate = 1/6 - 1/9 = 3/18 - 2/18 = 1/18 per hour. Tank fills in 18 hours.

Key Takeaways

  • Master the core concepts and formulas for Time & Work before attempting questions
  • Practice elimination strategy — rule out clearly wrong options first
  • Review explanations for every question, including those you answered correctly
  • This topic appears consistently in All Exams exams — expect 2-4 questions

Prepared for All Exams 2026 examination by GPT Sir. Visit gptsir.in for more practice material and AI-powered study assistance.