How to Solve Work, Efficiency and Wages Problems
Solve work-efficiency-and-wages aptitude problems using one-day-work fractions and proportional wage splitting, with a worked example.
Expected Interview Answer
Efficiency is inversely proportional to time taken alone, so a worker who finishes a job in fewer days has proportionally higher one-day work, and when the job is done jointly, wages split in the exact ratio of each worker’s one-day contribution to the total work.
Model the whole job as 1 unit of work. If A alone takes 'a' days, A’s one-day work is 1/a; the combined one-day work of several workers is the sum of their individual one-day work, and the job finishes when those fractions sum to 1. Efficiency ratio is simply the ratio of one-day-work fractions, which is the inverse of the ratio of days taken alone. When a payment is made for work done together, it is divided in the same ratio as each person’s contribution to the total work — not equally, and not by days worked, unless the days worked are identical for equal efficiency.
- One-day-work fractions unify time, efficiency and wage-sharing
- Efficiency ratio is the inverse of the days-alone ratio
- Same framework extends cleanly to teams and partial work
AI Mentor Explanation
A bowler who can dismiss a full order in 20 overs bowls at a higher “work rate” than one who needs 30 overs, and their efficiency ratio is 30:20, i.e. 3:2 — inverse of the overs each needs alone. If both bowl in the same spell and share a wicket-tally bonus, it should split 3:2, matching each bowler's actual contribution to the total wickets, not an even split. This one-day-work logic — fraction of the job done per unit time — is exactly how work-and-wages problems assign both time and payment.
Worked example (wage sharing)
One-day work
- A = 1/10, B = 1/15
Efficiency ratio
- 3/30 : 2/30 = 3:2
Wage split of 500
- A = 300, B = 200
Step-by-Step Explanation
Step 1
Convert days to one-day work
One-day work = 1 / (days taken alone) for each worker.
Step 2
Find the efficiency ratio
Express all one-day-work fractions with a common denominator, then compare numerators.
Step 3
Combine for joint completion time
Sum the one-day-work fractions; total days = 1 divided by that sum.
Step 4
Split wages by the same ratio
Divide any joint payment in the exact efficiency ratio, never equally unless the ratio is 1:1.
What Interviewer Expects
- Correct conversion of days alone into one-day-work fractions
- Recognizing efficiency ratio is the inverse of the days-alone ratio
- Correct combination of one-day-work fractions for joint completion time
- Wages split strictly by contribution ratio, not equally or by days worked
Common Mistakes
- Splitting wages equally regardless of differing efficiency
- Averaging days taken instead of summing one-day-work fractions
- Confusing efficiency ratio with the days-alone ratio (forgetting to invert)
- Ignoring partial days worked before a worker leaves the job
Best Answer (HR Friendly)
“I treat the whole job as one unit and find each person’s one-day-work as a fraction — one over the days they would take alone. Their efficiency ratio is just those fractions compared, which is the inverse of the ratio of days they take alone. When they get paid together for a joint job, I split the payment in that exact same efficiency ratio, because that is the true proportion of the work each person actually did.”
Follow-up Questions
- How do you handle wage sharing when a worker leaves before the job finishes?
- How does the one-day-work method extend to three or more workers?
- How would you find how many days B alone would take, given the combined rate and A alone?
- How does efficiency percentage (e.g. "A is 25% more efficient than B") translate into a time ratio?
MCQ Practice
1. A can finish a job alone in 12 days, B alone in 18 days. What is their efficiency ratio (A:B)?
One-day work: A = 1/12, B = 1/18. LCM 36 gives 3/36 and 2/36, so ratio A:B = 3:2.
2. A and B together earn 800 for a job. A alone takes 8 days, B alone takes 12 days. A's share is?
One-day work ratio A:B = 1/8 : 1/12 = 3:2. A's share = 800 × 3/5 = 480.
3. A is twice as efficient as B. If B alone takes 20 days, how many days does A alone take?
Twice the efficiency means half the time: A takes 20/2 = 10 days.
Flash Cards
One-day work formula? — If a worker takes n days alone, their one-day work is 1/n.
How is efficiency ratio found? — Compare one-day-work fractions; it is the inverse of the days-alone ratio.
How is joint payment split? — In the exact ratio of each worker's one-day-work contribution, not equally.
Combined completion time? — 1 divided by the sum of all workers' one-day-work fractions.