Lesson 5 � Intermediate
Time & Work
Time & work ek versatile topic hai � pipes & cisterns bhi isi pe based hai. Efficiency method seekho toh har problem 30 seconds mein solve hoga. Chalo LCM method dekhte hain.
Time & Work basics
WHAT
Agar A kaam 10 din mein karta hai aur B 15 din mein, toh dono milke kitne din mein karenge✓ Ye time-work ka basic sawal hai. Concept hai "work done per day" ka � efficiency.
WHEN
Workers, machines, pipes filling/emptying tanks � sab mein ye pattern hai. MNC exams mein 3-4 questions aate hain. Pipes & cisterns bhi isi type ka hai.
WHERE
LCM method sabse fast hai. Total work ko LCM lo, phir per day efficiency nikalo. Ye traditional fraction method se 3x fast hai.
Efficiency method
# Efficiency Method (LCM approach):
# Step 1: LCM of all days = Total Work
# Step 2: Individual efficiency = Total Work / Days
# Step 3: Combined efficiency = Sum of efficiencies
# Step 4: Time = Total Work / Combined Efficiency
# Example: A = 10 days, B = 15 days, C = 30 days
# LCM(10,15,30) = 30
# A efficiency = 30/10 = 3
# B efficiency = 30/15 = 2
# C efficiency = 30/30 = 1
# Combined = 3 + 2 + 1 = 6
# Time = 30/6 = 5 days
# If A and B work together:
# Time = Total / (effA + effB)
# = 30 / (3+2) = 30/5 = 6 daysAlternate work pattern
Kabhi kabhi A aur B alternate karte hain � pehle A, phir B, phir A. Ismein 2 din ka pattern dekho:
# Alternate work: A and B alternate, A starts
# 2-day pattern: A does 3 units + B does 2 units = 5 units
# Total work = 30 units
# After 12 days (6 cycles of 2 days): 6 � 5 = 30 units
# Answer: 12 days
# If total work was 28 units:
# After 10 days (5 cycles): 5 � 5 = 25 units
# Day 11: A does 3 units ✓ total 28 units
# Answer: 11 days
# Important: Always check karo last day pe kaun kaam kar raha haiPipes & Cisterns
Pipes & cisterns time-work ka extended version hai. Inlet pipe = filling (positive work), outlet pipe = emptying (negative work):
# Inlet pipe: Fills tank in X minutes
# Efficiency = 1/X (per minute)
# Outlet pipe: Empties tank in Y minutes
# Efficiency = -1/Y (per minute)
# Both open:
# Net efficiency = 1/X - 1/Y (if X < Y, tank fills)
# Net efficiency = 1/X - 1/Y (if X > Y, tank empties)
# Example: Pipe A fills in 10 min, Pipe B empties in 15 min
# Net efficiency = 1/10 - 1/15 = 3/30 - 2/30 = 1/30
# Time to fill = 30 minutes
# Shortcut: When both pipes open
# Time = (X � Y) / (Y - X) (if filling faster)
# Time = (X � Y) / (X - Y) (if emptying faster)Men, Women & Children problems
In problems mein efficiency alag-alag hoti hai. Pehle ek unit mein convert karo:
# Example: 5 men ya 10 women ya 20 children
# 1 kaam 10 din mein karte hain
# Let: 1 man = 2 children, 1 woman = 2 children
# 5 men = 10 children
# 10 women = 20 children
# Total = 10 + 20 + 20 = 50 children
# 20 children 10 din mein karte hain
# Total work = 50 � 10 = 500 child-days
# If 10 men + 5 women + 10 children = 20+10+10 = 40 children
# Time = 500/40 = 12.5 daysExercise
Question: A 10 din mein kaam karta hai, B 15 din mein. Dono milke kitne din mein karenge? (Sirf number)
Question: Pipe A tank 10 minute mein bharta hai, Pipe B 15 minute mein khali karta hai. Dono khule ho toh kitne minute mein bharega? (Sirf number)
Question: A aur B alternate karte hain, A pehle start karta hai. A 3 units/day karta hai, B 2 units/day karta hai. Total work 30 units hai. Kitne din mein hoga? (Sirf number)
Question: A 10 din mein, B 15 din mein, C 30 din mein. Teeno milke kitne din mein karenge? (Sirf number)
Common mistakes
- LCM method na use karna: Fractions se solve karna slow hai. Hamesha LCM method use karo � 3x fast hai.
- Alternate work mein last day check karna bhoolna: Hamesha dekho last cycle ke baad kaun kaam karega � A ya B.
- Pipes & cisterns mein outlet ka sign galat hona: Outlet pipe ka efficiency negative hai. Fill rate se subtract karo.
- "Together" ka matlab samajhna: "A and B together" = dono ek saath kaam kar rahe hain, alternate nahi.
Time & work samajh aa gaya✓ Ab Reasoning module shuru karte hain � Number Series se.