How to Solve Wages-Distribution-by-Work-Share Problems
Solve wages-distribution aptitude problems by proportional output share using rate × time worked, with a worked example and practice questions.
Expected Interview Answer
When workers combine on a job, total wages are split in direct proportion to each worker’s share of the actual work done, which is computed from their individual work rate multiplied by the time they actually worked, not from equal division or raw days alone.
The fair-split principle follows directly from the man-days idea: each worker’s contribution equals their rate (1/their-solo-time) multiplied by however long they actually worked, and the total wage is divided into these contribution ratios. Two workers with different efficiencies who work the same duration split wages in the ratio of their rates, since the faster worker produced proportionally more output. When workers join or leave at different times, compute each person’s total output share first (rate × their own working duration), form the ratio of shares, and distribute the wage accordingly. This same logic applies whether the payout is wages for labor, profit for a joint venture, or credit for a shared project — proportional output share is always the deciding factor, not equal split or time alone.
- One principle (share of output, not equal split) governs every variant
- Naturally extends to workers joining or leaving at different times
- Generalizes wages logic directly into partnership profit-sharing problems
AI Mentor Explanation
If a match fee is split between two bowlers based on wickets taken rather than overs bowled, a bowler who takes 6 of the 10 wickets earns 60% of the fee, even if both bowled the same number of overs. Wages-distribution problems work identically: pay is split by each worker’s proportional output — their rate times time worked — not by equal shares or by raw time alone. A faster worker who completes more of the job in the same time earns a proportionally larger cut.
Worked example (workers of different efficiency, different durations)
A’s output
- Rate 1/10 × 4 days = 0.4
B’s output
- Rate 1/15 × 6 days = 0.4
Wage split (2:2:1)
- A=1200, B=1200, C=600
Step-by-Step Explanation
Step 1
Find each worker's rate
Rate = 1 / (time to finish the job alone).
Step 2
Compute each worker's output share
Output share = rate × the duration that worker actually worked.
Step 3
Form the ratio
Express all output shares as a simplified whole-number ratio.
Step 4
Split the total payout
Divide the total wage/profit in that exact ratio.
What Interviewer Expects
- Correct computation of individual rates from solo completion times
- Correct output share as rate × actual time worked, not raw time
- Forming a clean ratio before splitting the payout
- Recognizing this generalizes to partnership profit-sharing
Common Mistakes
- Splitting wages equally regardless of differing output
- Splitting wages by time worked alone, ignoring differing efficiency
- Forgetting to account for a worker who joined late or left early
- Failing to simplify the output-share ratio before dividing the payout
Best Answer (HR Friendly)
“I always split wages by proportional output, never equally and never by raw time alone. I find each worker’s rate from how long they’d take the job solo, multiply by the time they actually worked to get their output share, then form the ratio of those shares across everyone involved. The total payout is divided in exactly that ratio, which is the same logic used later for partnership profit-sharing problems.”
Follow-up Questions
- How does this change if a worker is twice as efficient as stated, rather than a given solo time?
- How would you handle three workers joining and leaving at staggered times?
- How is this principle reused in partnership profit-sharing based on investment × time?
- What if the job isn't fully completed — how do you distribute a partial payout?
MCQ Practice
1. A can finish a job in 12 days, B in 8 days. They work together for the whole job. Wages of 1000 are split in the ratio?
A's rate = 1/12, B's rate = 1/8. Ratio = 1/12 : 1/8 = 2:3, so B earns more.
2. A works alone for 5 days on a job A can finish in 20 days, then B (who can finish alone in 15 days) completes the rest. A total payment of 900 is split by output share in ratio?
A's output = 5/20 = 0.25; remaining = 0.75 done by B, B's time = 0.75×15=11.25 days but output matters: ratio 0.25:0.75 = 1:3, closest simplified match is 3:8 is wrong; correct ratio is 1:3 which is choice index 1.
3. Three workers with output shares in ratio 3:4:5 split a total wage of 2400. The middle contributor receives?
Total parts = 12; each part = 200; middle contributor (4 parts) = 800.
Flash Cards
What decides the wage-split ratio? — Each worker's proportional output — rate × time actually worked.
How do faster workers get paid? — Proportionally more, since their rate produces more output in the same time.
What if workers join at different times? — Compute each person's output share individually before forming the ratio.
What later topic reuses this logic? — Partnership profit-sharing, based on investment × time instead of rate × time.