Efficiency — Faster Workers, Fewer Days
Efficiency — जो तेज़, उसके दिन कम
Efficiency — Faster Workers, Fewer Days
- Time & Work
- Efficiency — Faster Workers, Fewer Days
Convert efficiency statements into rate ratios and solve 'twice as good' problems.
🎯 Learning Objective
Convert efficiency statements into rate ratios and solve 'twice as good' problems.
💡 Concept
- Efficiency = work done per day → efficiency ∝ 1/time
- A twice as efficient as B → A takes HALF the days
- Efficiency ratio a : b → time ratio b : a (inverse)
- 'A is 50% more efficient' → efficiency 3 : 2 → time 2 : 3
🧮 Key Formulas
Efficiency ∝ 1/Time
>
Eff a : b ⇒ Time b : a
✏️ Easy Example
Q. A is twice as efficient as B. B alone can do a job in 12 days. In how many days can A do it?
- Double efficiency → half the time
- 12 ÷ 2 = 6
Answer: 6 days
🇮🇳 Real-Life Example
The ustad tailor stitches a blouse in 2 hours; his new assistant takes 4 — the master is exactly twice as efficient. Every workshop in India runs on this ratio.
📝 Exam-Level Example
Q. A is twice as good a workman as B, and together they finish a job in 14 days. In how many days can A alone finish it?
- Rates: A = 2 units, B = 1 unit → 3/day
- Total work = 3 × 14 = 42 units
- A alone: 42 ÷ 2 = 21
Answer: 21 days
📝 Exam-Level Example
Q. A can do a work in 15 days. B is 50% more efficient than A. In how many days will B finish it?
- B's rate = 1.5 × A's rate
- Time = 15 ÷ 1.5
Answer: 10 days
🪄 Memory Trick
Give the slowest worker 1 unit/day, scale the rest by the efficiency ratio, and count total units — the whole question becomes counting.
⚠️ Common Mistakes
- ❌ Halving the time when efficiency halves (time actually doubles)
- ❌ Reading '50% more efficient' as half the time — it means 2/3 of the time
🏆 Exam Tips
- ✅ Efficiency and time always move in opposite directions
- ✅ Flip the efficiency ratio to get the time ratio — nothing else changes
📌 Summary
- Efficiency ∝ 1/time
- Twice as good → half the days
- 50% more efficient → time × 2/3
- Unit rates make it a counting game