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
8graded MCQs · easy to hard · full solution & trap analysis
A worker earns ₹500 per day. If he works for 20 days, what is his total wage?
Practice 2easy
Two workers complete a job together in 8 days. If one worker earns ₹400 per day and the other earns ₹350 per day, what is the total wage paid to both workers?
Practice 3easy
A worker completes 1/4 of a job in 5 days at ₹600 per day. What is the total wage he will receive for completing the entire job at the same rate?
Practice 4medium
A worker is paid ₹500 per day. If he works for 12 days, what is his total wage?
Practice 5medium
Two workers A and B complete a job together in 8 days. If A is paid ₹400 per day and B is paid ₹350 per day, what is their combined daily wage?
Practice 6medium
A tailor completes 5 shirts per day and earns ₹300 per shirt. How much does he earn in 6 days?
Practice 7medium
Three workers share ₹2400 wages for completing a project in proportion to the days they worked: 10 days, 8 days, and 6 days respectively. How much does the worker who worked 10 days receive?
Practice 8hard
A and B together can complete a job in 12 days. A's daily wage is ₹500 and B's daily wage is ₹700. If they work together for the entire 12 days, what is the total amount paid to both of them?
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