Core ConceptRead this first — the foundation of the topic
Core Concept
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.
Formula BlockMemorise — 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
Exam PatternsWhat 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.
ShortcutsUse 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).
Worked ExampleSolve 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)
Exam TrapsCommon mistakes students make — avoid these
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 to Remember
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-Specific Tips
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
Practice MCQs
Work & Wages — Practice Questions
10graded MCQs · easy to hard · full solution & trap analysis
A job is worth ₹12000. Worker P completes 1/3 of the job and Worker Q completes the remaining 2/3. How much should Q be paid if wages are distributed proportionally to work done?
Practice 2easy
A worker is paid ₹500 per day. If he works for 12 days, what is his total wage?
Practice 3easy
A worker earns ₹8000 per month. If he works for 3 months and 15 days (assume 1 month = 30 days), what is his total earnings?
Practice 4easy
Three workers X, Y, and Z complete a task and share ₹3600 in the ratio 1:2:3. How much does Z receive?
Practice 5easy
A man completes a job in 10 days and is paid ₹5000 for the entire job. What is his daily wage?
Practice 6easy
Two workers, A and B, are paid in the ratio 3:5. If A receives ₹2400, how much does B receive?
Practice 7medium
A contractor hires workers to complete a project. If he hires 8 workers, the project takes 15 days. If he hires 12 workers, the project takes 10 days. However, due to inefficiency, the actual work done is only 80% of the expected work. How many days will 10 workers take to complete the project at 80% efficiency?
Practice 8medium
A task requires 240 worker-days to complete. If 6 workers are assigned and each worker is paid ₹500 per day, but due to poor management, only 75% of the expected work is completed in 30 days, how much total wages were paid?
Practice 9medium
A and B together earn ₹1,360 for completing a job. A works for 8 hours and B works for 6 hours. If A's hourly rate is ₹80 per hour, what is B's hourly rate?
Practice 10hard
A contractor hires workers on the condition that they receive ₹500 per day for work and lose ₹100 per day for absence. After 30 days, a worker receives ₹11,400. How many days did the worker actually work?
60-Second Revision — Work & Wages
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