When multiple people work together and complete a job, their wages should be divided in the ratio of their work rates or efficiency. If A can do work in 10 days and B in 15 days, A is more efficient and deserves higher wages
💡Key Rules
(1) Wages ∝ Work Rate (2) Wages ∝ 1/Time taken (3) Total wages = Sum of individual wages (4) If workers work for different durations, wages depend on both efficiency and time worked.
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Formula Block
Memorise — at least one formula appears in every paper
Wage Ratio = Work Rate Ratio = 1/Time Ratio
A's wage : B's wage = (1/A's time) : (1/B's time)
If working together: Combined rate = 1/A + 1/B
Wage distribution = (Individual rate / Combined rate) × Total wages
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Exam Patterns
What examiners ask — read before attempting PYQs
SSC CGL frequently asks wage distribution problems with 2-3 workers having different efficiencies. Common variations include workers joining/leaving at different times, and finding individual wages from total payment.
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Shortcuts
Use these to save 30–60 seconds per question
For time-based problems, flip the time values to get wage ratios directly. If A takes 6 days and B takes 9 days, wage ratio = 9:6 = 3:2 (notice the flip).
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Worked Example
Solve this step-by-step before moving on
1
Step 1
Find work rates
A's rate = 1/12 work per day
B's rate = 1/15 work per day
2
Step 2
Calculate wage ratio
Wage ratio = Rate ratio = (1/12) : (1/15)
Taking LCM of 12 and 15 = 60
(1/12) = 5/60 and (1/15) = 4/60
So ratio = 5:4
3
Step 3
Distribute wages
Total parts = 5 + 4 = 9
A's wage = (5/9) × 1350 = Rs 750
B's wage = (4/9) × 1350 = Rs 600
Verification: 750 + 600 = 1350 ✓
Shortcut for this: Time ratio = 12:15 = 4:5, so wage ratio = 5:4 (flipped)
Common Mistake: Students often forget to flip time ratios when calculating wage ratios. Remember: higher efficiency (less time) means higher wages. Also, when workers work for different durations, multiply efficiency by time worked to get actual work contribution.
🔑 Key Points
Wages are always proportional to work rate or efficiency of workers
Wage ratio = 1/Time ratio (flip the time values to get wage ratio)
If A takes 'm' days and B takes 'n' days, wage ratio = n:m
Combined work rate = sum of individual work rates
When workers work different hours, multiply rate by time for wage calculation
Total wages distributed = sum of all individual wages
Higher efficiency worker gets larger share of wages
Wage distribution formula: (Individual rate/Total rate) × Total wages
📌 Exam Facts
Work rate is always reciprocal of time taken (Rate = 1/Time)
Wage ratio equals work rate ratio in direct proportion
LCM method used to compare fractions in work rate calculations
Combined efficiency = sum of individual efficiencies when working together
Time ratio and wage ratio are inverse to each other
Proportion formula: A:B = x:y means A/B = x/y
Work done = Rate × Time for individual contribution calculation
🚀 60-Second Revision
Remember: Wage ratio = 1/Time ratio (always flip time values)
Formula: Individual wage = (Own rate/Combined rate) × Total wages
Trick: For times a:b, wages will be b:a
Trap: Don't forget to multiply by working hours if different
Quick check: Sum of distributed wages = Total wages given
Pattern: Higher efficiency = Less time = More wages
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Test yourself under real exam conditions
A timed ITBP Constable mock shows exactly how Work & Wages questions appear in the actual paper — and where you lose marks.