📑 Topics on this page (Jump to Topic):
📌 1. LCM (Total Work) Method
- Take total work = LCM of the days; one day's work (efficiency) = total work/days.
- A alone a days, B alone b days → together = ab/(a + b) days.
- For A, B, C: together = 1/(1/a + 1/b + 1/c).
✏️ Example: A 12 days, B 18 days. Total = 36; A = 3/day, B = 2/day → together 36/5 = 7.2 days.
📌 2. M × D × H Formula & Efficiency
📘 Formulas:
- M₁D₁H₁/W₁ = M₂D₂H₂/W₂ (M = men, D = days, H = hours/day, W = work)
- If A is k times as efficient as B, A takes 1/k of B's time
- Wages are shared in the ratio of work done (efficiency × days)
⚠️ Exam Traps:
- "A is 50% more efficient than B" → efficiency 3 : 2, time 2 : 3.
- Wages are shared by work done, not by number of days.
📌 3. Practice MCQs
📝 Practice MCQs (prepared by SF Prep — not PYQs)
Q1. A can do a work in 36 days and B in 10 days. In how many days will they finish it together? Practice
Correct answer: (B)
Solution: Total work = LCM(36, 10) = 180; efficiency 5 + 18 = 23; time = 180⁄23 = 180⁄23 days.
Solution: Total work = LCM(36, 10) = 180; efficiency 5 + 18 = 23; time = 180⁄23 = 180⁄23 days.
Q2. A, B and C can do a work in 24, 10 and 20 days respectively. In how many days will all three together finish it? Practice
Correct answer: (C)
Solution: Total = 120; efficiencies 5, 12, 6 (sum 23) → 120⁄23 = 120⁄23 days.
Solution: Total = 120; efficiencies 5, 12, 6 (sum 23) → 120⁄23 = 120⁄23 days.
Q3. A and B together finish a work in 12 days. A alone can do it in 15 days. In how many days can B alone do it? Practice
Correct answer: (D)
Solution: B = 1/(1⁄12 − 1⁄15) = 12×15/(15 − 12) = 60 days.
Solution: B = 1/(1⁄12 − 1⁄15) = 12×15/(15 − 12) = 60 days.
Q4. A and B can do a work in 24 and 15 days respectively. They start together, but A leaves after 4 days. In how many days will B finish the remaining work? Practice
Correct answer: (A)
Solution: Total = 120; in 4 days (5 + 8) × 4 = 52; remaining 68; B = 68⁄8 = 8.5 days.
Solution: Total = 120; in 4 days (5 + 8) × 4 = 52; remaining 68; B = 68⁄8 = 8.5 days.
Q5. 12 men working 8 hours a day finish a job in 20 days. In how many days will 8 men working 6 hours a day finish it? Practice
Correct answer: (B)
Solution: M₁D₁H₁ = M₂D₂H₂ → D₂ = 12×20×8/(8×6) = 40 days.
Solution: M₁D₁H₁ = M₂D₂H₂ → D₂ = 12×20×8/(8×6) = 40 days.
Q6. A is 25% more efficient than B. B alone does a work in 20 days. In how many days will A alone do it? Practice
Correct answer: (C)
Solution: Efficiency A : B = 125 : 100 → time A : B = 100 : 125 → A = 20 × 100⁄125 = 16 days.
Solution: Efficiency A : B = 125 : 100 → time A : B = 100 : 125 → A = 20 × 100⁄125 = 16 days.
Q7. A can do a work in 4 days and B in 6 days. They work on alternate days, A starting first. In how many days will the work be completed? Practice
Correct answer: (D)
Solution: Total = 12; every 2 days 3 + 2 = 5; 2 cycles (4 days) give 10, remaining 2 → 14⁄3 days in all.
Solution: Total = 12; every 2 days 3 + 2 = 5; 2 cycles (4 days) give 10, remaining 2 → 14⁄3 days in all.
Q8. A can do a work in 36 days and B in 24 days. In how many days will they finish it together? Practice
Correct answer: (A)
Solution: Total work = LCM(36, 24) = 72; efficiency 2 + 3 = 5; time = 72⁄5 = 14.4 days.
Solution: Total work = LCM(36, 24) = 72; efficiency 2 + 3 = 5; time = 72⁄5 = 14.4 days.
Q9. A, B and C can do a work in 15, 12 and 40 days respectively. In how many days will all three together finish it? Practice
Correct answer: (B)
Solution: Total = 120; efficiencies 8, 10, 3 (sum 21) → 120⁄21 = 40⁄7 days.
Solution: Total = 120; efficiencies 8, 10, 3 (sum 21) → 120⁄21 = 40⁄7 days.
Q10. A and B together finish a work in 30 days. A alone can do it in 40 days. In how many days can B alone do it? Practice
Correct answer: (C)
Solution: B = 1/(1⁄30 − 1⁄40) = 30×40/(40 − 30) = 120 days.
Solution: B = 1/(1⁄30 − 1⁄40) = 30×40/(40 − 30) = 120 days.
Q11. A and B can do a work in 24 and 20 days respectively. They start together, but A leaves after 2 days. In how many days will B finish the remaining work? Practice
Correct answer: (D)
Solution: Total = 120; in 2 days (5 + 6) × 2 = 22; remaining 98; B = 98⁄6 = 49⁄3 days.
Solution: Total = 120; in 2 days (5 + 6) × 2 = 22; remaining 98; B = 98⁄6 = 49⁄3 days.
Q12. 10 men working 6 hours a day finish a job in 24 days. In how many days will 20 men working 9 hours a day finish it? Practice
Correct answer: (A)
Solution: M₁D₁H₁ = M₂D₂H₂ → D₂ = 10×24×6/(20×9) = 8 days.
Solution: M₁D₁H₁ = M₂D₂H₂ → D₂ = 10×24×6/(20×9) = 8 days.
Q13. A is 50% more efficient than B. B alone does a work in 36 days. In how many days will A alone do it? Practice
Correct answer: (B)
Solution: Efficiency A : B = 150 : 100 → time A : B = 100 : 150 → A = 36 × 100⁄150 = 24 days.
Solution: Efficiency A : B = 150 : 100 → time A : B = 100 : 150 → A = 36 × 100⁄150 = 24 days.
Q14. A can do a work in 10 days and B in 12 days. They work on alternate days, A starting first. In how many days will the work be completed? Practice
Correct answer: (C)
Solution: Total = 60; every 2 days 6 + 5 = 11; 5 cycles (10 days) give 55, remaining 5 → 65⁄6 days in all.
Solution: Total = 60; every 2 days 6 + 5 = 11; 5 cycles (10 days) give 55, remaining 5 → 65⁄6 days in all.
Q15. A can do a work in 40 days and B in 15 days. In how many days will they finish it together? Practice
Correct answer: (D)
Solution: Total work = LCM(40, 15) = 120; efficiency 3 + 8 = 11; time = 120⁄11 = 120⁄11 days.
Solution: Total work = LCM(40, 15) = 120; efficiency 3 + 8 = 11; time = 120⁄11 = 120⁄11 days.
Q16. A, B and C can do a work in 12, 20 and 60 days respectively. In how many days will all three together finish it? Practice
Correct answer: (A)
Solution: Total = 60; efficiencies 5, 3, 1 (sum 9) → 60⁄9 = 20⁄3 days.
Solution: Total = 60; efficiencies 5, 3, 1 (sum 9) → 60⁄9 = 20⁄3 days.
Q17. A and B can do a work in 15 and 24 days respectively. They start together, but A leaves after 2 days. In how many days will B finish the remaining work? Practice
Correct answer: (B)
Solution: Total = 120; in 2 days (8 + 5) × 2 = 26; remaining 94; B = 94⁄5 = 18.8 days.
Solution: Total = 120; in 2 days (8 + 5) × 2 = 26; remaining 94; B = 94⁄5 = 18.8 days.
Q18. A is 20% more efficient than B. B alone does a work in 24 days. In how many days will A alone do it? Practice
Correct answer: (C)
Solution: Efficiency A : B = 120 : 100 → time A : B = 100 : 120 → A = 24 × 100⁄120 = 20 days.
Solution: Efficiency A : B = 120 : 100 → time A : B = 100 : 120 → A = 24 × 100⁄120 = 20 days.
Q19. A can do a work in 12 days and B in 5 days. They work on alternate days, A starting first. In how many days will the work be completed? Practice
Correct answer: (D)
Solution: Total = 60; every 2 days 5 + 12 = 17; 3 cycles (6 days) give 51, remaining 9 → 22⁄3 days in all.
Solution: Total = 60; every 2 days 5 + 12 = 17; 3 cycles (6 days) give 51, remaining 9 → 22⁄3 days in all.
Q20. A, B and C can do a work in 40, 60 and 10 days respectively. In how many days will all three together finish it? Practice
Correct answer: (A)
Solution: Total = 120; efficiencies 3, 2, 12 (sum 17) → 120⁄17 = 120⁄17 days.
Solution: Total = 120; efficiencies 3, 2, 12 (sum 17) → 120⁄17 = 120⁄17 days.