Study Material — 1 PYQs (2021–2021) · Concept Notes · Shortcuts
SBI PO Efficiency Problems is a frequently tested subtopic — 1 previous year questions from 2021–2021 papers are included below with concept notes, key rules and shortcut tricks.
1 questions from actual SBI PO papers · all shown free · click option to reveal solution
Exam Q 12021Previous Year Pattern
The efficiency of X is 25% more than Y. If X and Y together can complete a project in 10 days, in how many days can X alone complete the project?
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