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AFCAT Efficiency Problems

Study Material — 1 PYQs (2020–2020) · Concept Notes · Shortcuts

AFCAT Efficiency Problems is a frequently tested subtopic — 1 previous year questions from 2020–2020 papers are included below with concept notes, key rules and shortcut tricks.

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2020–2020
18 Practice
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8 Key Points
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Previous Year Questions

AFCAT Efficiency Problems — Past Exam Questions

1 questions from actual AFCAT papers · all shown free · click option to reveal solution

Exam Q 12020Previous Year Pattern

A and B together can complete a project in 12 days. A's efficiency is 25% more than B's efficiency. If A and B work together for 8 days and then B leaves, how many more days will A alone take to finish the remaining work?

Concept Notes

Efficiency Problems— Rules & Concept

1.Core Concept

Read 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.

2.Formula Block

Memorise — 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.

3.Exam Patterns

What 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.

4.Worked Example

Solve 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.

5.Exam Traps

Common 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

18graded MCQs · easy to hard · full solution & trap analysis

All MCQs →
Practice 1easy

P can do 1/4 of a work in 5 days. Q can do 1/3 of the same work in 4 days. Who is more efficient, and by what percentage?

Practice 2easy

The efficiency of A is twice the efficiency of B. If A can complete a task in 10 days, how many days will B take to complete the same task?

Practice 3easy

A can do 1/3 of a work in 5 days. In how many days can A complete the entire work?

Practice 4easy

N can do 2/5 of a job in 8 days. How many days will N take to complete the entire job?

Practice 5easy

M can complete 1/4 of a work in 5 days. At this rate, in how many days will M complete the entire work?

Practice 6medium

The efficiency of X is 25% more than Y. If X and Y together can complete a job in 10 days, in how many days can X alone complete the job?

Practice 7medium

A's work rate is twice that of B. If A and B working together can finish a task in 9 days, how many days will A take working alone?

Practice 8medium

The efficiency of X is 25% more than Y. If X and Y together can complete a job in 10 days, how many days will X alone take to complete the job?

Practice 9hard

A can do a piece of work in 16 days. B can do the same work in 20 days. They work together for some days, then A leaves and B continues alone for 4 more days to complete the work. For how many days did A and B work together?

Practice 10hard

A can complete a work in 12 days. B is 50% more efficient than A. C is 25% less efficient than B. If A, B, and C work together for 2 days, then B and C work together for 3 days, how much work remains?

Practice 11hard

A is twice as efficient as B. B is thrice as efficient as C. If A, B, and C working together can complete a task in 6 days, in how many days can A alone complete the task?

Practice 12hard

A, B, and C can complete a project in 18, 24, and 36 days respectively. They work together for some days, then A leaves. B and C continue for 4 more days and complete the project. For how many days did all three work together?

Practice 13hard

A can do a work in 16 days. B can do the same work in 20 days. A starts the work alone for 4 days, then B joins A. After B joins, their combined efficiency increases by 25% due to better coordination. In how many more days will the work be completed?

Practice 14hard

A can complete a work in 12 days. B is 50% more efficient than A. C is 25% less efficient than B. If all three work together for 4 days, then A and B work together for 2 more days, how much work remains?

Practice 15hard

Two pipes A and B can fill a tank in 20 hours and 30 hours respectively. A drain pipe C can empty the full tank in 40 hours. If A and B are opened together for 6 hours, then C is also opened, and all three run together, how long will it take to fill the remaining tank?

Practice 16hard

A, B, and C can complete a project in 18, 24, and 36 days respectively. They start working together, but after 3 days, A leaves. After 2 more days, B also leaves. C continues alone. How many more days does C need to finish the project?

Practice 17hard

Two pipes A and B can fill a tank in 20 hours and 30 hours respectively. A drain pipe C can empty the full tank in 40 hours. If A and B are opened for 5 hours, then C is also opened, and all three run together, in how many more hours will the tank be full?

Practice 18hard

X can complete a work in 30 days. Y can complete the same work in 40 days. They work together for 10 days, then X leaves. Y continues for 5 more days. Z joins and they complete the remaining work in 3 days. In how many days can Z alone complete the entire 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
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