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
7graded MCQs · easy to hard · full solution & trap analysis
If 8 workers can build a wall in 15 days, how many days will 12 workers take to build the same wall?
Practice 2easy
Three workers are paid in the ratio 3:4:5 for a job. If the total payment is ₹2400, how much does the worker with the highest share receive?
Practice 3easy
A and B together earn ₹1200 in 5 days. If A earns ₹40 per day and B earns ₹50 per day, how much will they earn together in 8 days?
Practice 4easy
A worker is paid ₹500 for completing a job in 5 days. If he works for 8 days at the same rate, how much will he earn?
Practice 5easy
A contractor pays ₹2400 to 6 workers for 4 days of work. What is the daily wage per worker?
Practice 6medium
A contractor hires 8 workers to complete a project in 24 days. After 6 days, he hires 4 more workers. If all workers are paid equally at ₹500 per day, how much more will the contractor pay in total wages compared to hiring only the original 8 workers for the full 24 days?
Practice 7hard
A contractor hires workers at ₹500 per day. If 8 workers can complete a job in 18 days, how many workers must be hired to complete the same job in 12 days, keeping the daily wage unchanged? What is the additional cost incurred?
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