Study Material — 3 PYQs (2018–2021) · Concept Notes · Shortcuts
RRB NTPC Efficiency Problems is a frequently tested subtopic — 3 previous year questions from 2018–2021 papers are included below with concept notes, key rules and shortcut tricks.
RRB NTPC Efficiency Problems — Past Exam Questions
3 questions from actual RRB NTPC papers · all shown free · click option to reveal solution
Exam Q 12021Previous Year Pattern
The work efficiency of A is 3 times that of B. If A and B together complete a project in 9 days, how many days will B alone take to complete the project?
Exam Q 22018Previous Year Pattern
A's efficiency is twice that of B. If A and B together can complete a project in 9 days, how many days will B alone take to complete it?
Exam Q 32021Previous Year Pattern
A contractor hires workers to complete a bridge in 20 days. After 5 days, he realizes the work is only 15% complete. He then increases the workforce by 60%. How many additional days beyond the original 20 days will be needed to finish 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
Practice MCQs
Efficiency Problems — Practice Questions
8graded 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, assuming all workers have equal efficiency?
Practice 2easy
A's work efficiency is twice that of B. If A alone can complete a task in 9 days, how many days will B take to complete the same task?
Practice 3easy
The efficiency of X is twice the efficiency of Y. If X alone can complete a job in 9 days, how many days will Y take to complete the same job?
Practice 4easy
P can do 1/4 of a work in 5 days. At this rate, how many days will P take to complete the entire work?
Practice 5medium
The efficiency of worker M is 25% more than worker N. If M and N together can complete a job in 12 days, how many days will N alone take to complete the job?
Practice 6hard
A contractor hires workers such that the work efficiency increases by 20% every day. On day 1, the workers complete 10 units of work. If the total work required is 132 units, on which day will the work be completed?
Practice 7hard
A work is completed by 8 men in 10 days. If the work is to be completed in 5 days, how many additional men are needed, assuming all men work at the same efficiency?
Practice 8hard
Machine A produces 240 units per hour. Machine B produces 30% more units per hour than A. If both machines run together for 5 hours, then only B runs for 3 more hours, what is the total production?
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