Study Material — 2 PYQs (2020–2020) · Concept Notes · Shortcuts
SSC CPO Efficiency Problems is a frequently tested subtopic — 2 previous year questions from 2020–2020 papers are included below with concept notes, key rules and shortcut tricks.
2 questions from actual SSC CPO papers · all shown free · click option to reveal solution
Exam Q 12020Previous Year Pattern
A's efficiency is 25% more than B's. If A and B together complete a task in 9 days, how many days does B alone need to complete the task?
Exam Q 22020Previous Year Pattern
A team of workers can complete a project in 30 days. After 10 days of work, the team's efficiency increases by 25%. The project is then completed in 12 more days. If the project had been completed at the original efficiency throughout, how many days would it have taken?
Concept Notes
Efficiency Problems— Rules & Concept
Core ConceptRead this first — the foundation of the topic
Efficiency in Time & Work represents how much work a person can complete in unit time. Think of efficiency as work rate or speed of work. If Ram can finish a job in 10 days, his efficiency is 1/10 of the total work per day. This concept forms the backbone of most SSC CGL Time & Work problems. Key Rules: Total Work = Efficiency × Time. When workers combine, their efficiencies add up. If A's efficiency is 1/12 and B's efficiency is 1/15, together they work at (1/12 + 1/15) efficiency. The reciprocal of combined efficiency gives combined time.
Formula BlockMemorise — at least one formula appears in every paper
Individual Efficiency = 1/Time taken. Combined Efficiency = Sum of individual efficiencies. Time for combined work = 1/Combined Efficiency. Work Ratio = Efficiency Ratio = Inverse of Time Ratio.
Exam PatternsWhat examiners ask — read before attempting PYQs
Common types include
workers joining/leaving at different times, comparing work rates, finding individual efficiencies when combined time is given, and efficiency ratios. Questions often involve 2-3 workers with fractional efficiencies
Powerful Shortcut
LCM Method. Take LCM of all given times as total work units. Each person's efficiency becomes LCM/their time. This eliminates fractions completely and makes calculations super fast.
Worked ExampleSolve this step-by-step before moving on
1
Step 1
Find LCM of 15 and 20 = 60 (assume total work = 60 units)
2
Step 2
A's efficiency = 60/15 = 4 units per day
3
Step 3
B's efficiency = 60/20 = 3 units per day
4
Step 4
Combined efficiency = 4 + 3 = 7 units per day
5
Step 5
Combined time = 60/7 = 8(4/7) days
Alternative method: A's efficiency = 1/15, B's efficiency = 1/20. Combined = 1/15 + 1/20 = (4+3)/60 = 7/60. Time = 1/(7/60) = 60/7 days.
Another Trick: For two workers, combined time = (Product of individual times)/(Sum of individual times). Here: (15×20)/(15+20) = 300/35 = 60/7 days.
Exam TrapsCommon mistakes students make — avoid these
Students often forget that when efficiency increases, time decreases proportionally. Also, they add times instead of adding efficiencies when workers combine. Remember: efficiencies add up, not times.
Key Points to Remember
Efficiency = 1/Time taken by individual worker
When workers combine, their efficiencies get added
Combined time = 1/(Sum of individual efficiencies)
Work ratio equals efficiency ratio equals inverse of time ratio
LCM method eliminates fractions and speeds up calculations
For two workers: Combined time = (Product of times)/(Sum of times)
Higher efficiency means lower time taken for same work
Total work = Efficiency × Time for any worker
Exam-Specific Tips
Combined efficiency formula for two workers: 1/T1 + 1/T2
Work ratio formula: W1:W2 = E1×t1 : E2×t2
Efficiency is always expressed as fraction of total work per unit time
When efficiency doubles, time becomes half for same work
LCM method: Total work = LCM of all given individual times
Two workers formula: Combined time = (T1×T2)/(T1+T2)
If A is twice as efficient as B, then A:B efficiency ratio = 2:1
Efficiency and time are inversely proportional for same work
60-Second Revision — Efficiency Problems
Remember: Efficiencies add up when workers combine, times don't
Formula: Combined time for two workers = (T1×T2)/(T1+T2)
Trick: Use LCM method to avoid fractions in calculations
Trap: Don't confuse work ratio with time ratio - they're inverse
Quick check: Higher efficiency always means lower time
Pattern: Most SSC questions involve 2-3 workers with simple time values
Shortcut: Efficiency ratio = Inverse of time ratio