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Efficiency Problems

ITBP Constable · Quantitative Aptitude

Also prepare for:CRPF Const BSF Const CISF Const UP Const

← Pipes & Cisterns

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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.

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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.

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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.

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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. Common Mistake: 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

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 Facts

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

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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