🎙 Teacher-Style Introduction

Time & Work वह chapter है जिसमें सिर्फ एक ही concept चलता है — Efficiency = Work / Time. Delhi Police Constable exam में हर साल 2–3 आसान प्रश्न आते हैं।

“More work → more time, More workers → less time” यही पूरा logic है।

📘 Important Formulas / महत्वपूर्ण सूत्र

• Work = Time × Efficiency
• Time = Work / Efficiency
• Efficiency ∝ 1/Time
• If A does work in ‘a’ days ⇒ 1 day work = 1/a
• A & B together: (1/a + 1/b)
• LCM Method: Take LCM of days = Total Work

• कार्य = समय × दक्षता
• समय = कार्य / दक्षता
• A एक दिन में जितना काम करे = 1/a
• साथ में काम: 1/a + 1/b
• LCM method सबसे तेज़ तरीका है

⚡ Tricks & Shortcuts

• Always use LCM method → fastest in exam.
• 1 day work निकालकर जल्दी जोड़–घटाव करना आसान होता है।
• More workers → less time (inverse relation).
• DP exam में pipes/tanks type tricky questions नहीं आते।

✔ Solved Examples / हल प्रश्न

Example 1: A does a work in 10 days. Find 1-day work.
→ 1 day work = 1/10

Example 2: A = 10 days, B = 20 days. Find together time.
LCM = 20
A = 2 units/day, B = 1 unit/day
Total = 3 units/day → Time = 20/3 = 6.67 days

Example 3: A = 5 days, B = 15 days. Together?
LCM=15
A=3 units/day, B=1 unit/day
Total=4 units/day → Time=15/4=3.75 days

Example 4: A works 2× faster than B. If B takes 12 days, find A’s days.
A = half time → 6 days

Example 5: A: 12 days, B: 6 days. A works alone for 2 days, remaining?
LCM=12
A=1 unit/day → 2 units done
Remaining = 10 units
B=2 units/day → Time = 10/2 = 5 days

Example 6: A, B, C can do work in 10, 20, 30 days. Together?
LCM=60
Work/day = 6+3+2=11
Time = 60/11 = 5.45 days

Example 7: 4 men take 12 days. 6 men required?
Men ∝ 1/Days
6 men → 4×12/6 = 8 days

Example 8: A does 1/3 work in 4 days. Total days?
1/3 → 4 days
Full → 12 days

✔ MCQs (Delhi Police Pattern)

1. A=10 days, B=30 days. Together? Ans: 7.5 days
2. A=8 days, B=4 days. Together? Ans: 2.66 days
3. A alone=12 days, B alone=6 days → B efficiency? Ans: 2× A
4. A=20 days → 1 day work? Ans: 1/20
5. Work=60 units, efficiency=5 → days? Ans: 12
6. A=5 days, B=10 days → together? Ans: 3.33 days
7. 3 men → 15 days. 5 men → ? Ans: 9 days
8. A does 25% work in 5 days → full? Ans: 20 days
9. A=18 days, B=9 days → efficiency ratio? Ans: 1 : 2
10. A & B together=4 days, A=12 days → B=? Ans: 6 days

💡 Motivation: Time & Work sikha deta है — हर रोज थोड़ा-थोड़ा करो, बड़ा काम भी आसान हो जाता है. यही officer attitude है! 🚓🔥