Introduction
Time & Work problems compare how fast different people (or machines) complete a job. The efficiency
method — assuming total work = LCM of the given days — turns messy fractions into clean whole-number
arithmetic and is the standard bank-exam approach.
The Efficiency Method
1. Assume Total Work = LCM of all given time values (in units).
2. Efficiency (work/day) of each person = Total Work ÷ their number of days.
3. Combine efficiencies for people working together, then Time = Total Work ÷ Combined Efficiency.
Q. A can complete a work in 12 days and B in 18 days. In how many days will they finish it working together?
Total work = LCM(12,18) = 36 units. A's efficiency = 36/12 = 3 units/day. B's efficiency = 36/18 = 2 units/day.
Combined = 5 units/day. Time = 36/5 = 7.2 days.
Q. A, B and C together earn ₹1,800 for a job. A can do it alone in 10 days, B in 15 days, and C in 30 days. Find A's share of the wages.
Total work = LCM(10,15,30) = 30. Efficiencies: A=3, B=2, C=1 → ratio 3:2:1, total parts = 6.
Wages are shared in the efficiency ratio: A's share = (3/6) × 1800 = ₹900.
⚠️ Key Insight: Wages are always divided in the ratio of work done
(efficiency), not in the ratio of time taken — a slower worker (more days) gets a smaller wage share.
💡 Exam Tip: For "A and B start together, but A leaves after some days" type problems, calculate
work done by both together up to that point, then let the remaining person finish the rest alone using their own
efficiency.
✅ Practice Focus: LCM-based efficiency method · Work-wages ratio · Partial work / person leaving
mid-way problems.