DEFINITION
One-Line Definition
Work equals Efficiency (Rate of Work per unit time) multiplied by Time taken (Work = Efficiency × Time).
Inverse Property: Efficiency = 1 / Time (Faster worker = Higher efficiency)
CORE INTUITION 🧱
Brick Laying Mental Model
Assume total job is laying 36 bricks (LCM of 12 and 18):
- • Worker A takes 12 days → Rate = 36 / 12 = 3 bricks/day
- • Worker B takes 18 days → Rate = 36 / 18 = 2 bricks/day
- • Combined Rate = 3 + 2 = 5 bricks/day → 36 / 5 = 7.2 days
Always assume Total Work = LCM of individual times to avoid messy fractions!
💡 WHY THIS CONCEPT MATTERS & REAL-LIFE APPLICATIONS
Time & Work is a core arithmetic topic tested directly and indirectly across speed & logic exams. Click on any connected topic to jump directly to its Vault page:
Where Is Time & Work Used?
🏗️ Construction Planning
👥 Workforce Allocation
🏭 Factory Production
⏱️ Task Deadlines
📐 KEY FORMULAS & LCM METHOD
GOLDEN WORK EQUATION
Total Work = Efficiency (Rate) × Time
Efficiency = Total Work / Time | Time = Total Work / Efficiency
The Man-Days-Hours Chain Rule Formula
(M1 × D1 × H1) / W1 = (M2 × D2 × H2) / W2
Where M = number of workers, D = days, H = hours per day, W = total work completed.
📝 SOLVED EXAMPLES (LEVEL 0 TO ADVANCED)
EASY • EXAMPLE 1
A can finish a work in 10 days, and B can finish the same work in 15 days. How long will they take together?
Solution (LCM Method):
LCM of (10, 15) = 30 units (Total Work)
A's Efficiency = 30 / 10 = 3 units/day
B's Efficiency = 30 / 15 = 2 units/day
Combined Efficiency = 3 + 2 = 5 units/day
Time Together = 30 / 5 = 6 days
Answer: 6 days
MEDIUM • EXAMPLE 2
A and B together take 12 days to complete a job. A alone takes 20 days. How long will B alone take?
Solution:
LCM of (12, 20) = 60 units (Total Work)
Combined Rate (A+B) = 60 / 12 = 5 units/day
A's Rate = 60 / 20 = 3 units/day
B's Rate = (A+B) - A = 5 - 3 = 2 units/day
Time for B = 60 / 2 = 30 days
Answer: 30 days
HARD • EXAMPLE 3
12 men can complete a project in 16 days working 8 hours/day. How many days will 16 men take working 6 hours/day?
Solution (Man-Days Formula):
M1 × D1 × H1 = M2 × D2 × H2
12 × 16 × 8 = 16 × D2 × 6
1536 = 96 × D2
D2 = 1536 / 96 = 16 days
Answer: 16 days
⚠️ COMMON MISTAKES TO AVOID
❌ Mistake 1: Adding days directly
Never add days together! (If A takes 10 days and B takes 15 days, working together takes LESS than 10 days, NOT 25 days!).
❌ Mistake 2: Confusing Efficiency ratio with Time ratio
If A is twice as efficient as B, Efficiency Ratio (A:B) = 2:1, but Time Ratio (A:B) = 1:2.
🚀 CAT & MBA CET SHORTCUTS
⚡ Shortcut 1: Two-Worker Formula
If A takes X days and B takes Y days, combined time = (X × Y) / (X + Y). E.g. (10 × 15) / 25 = 6 days!
⚡ Shortcut 2: Alternate Days Shift Rule
Calculate work completed in one 2-day cycle (A on Day 1, B on Day 2), then multiply cycles until work is almost finished.
🎯 PRACTICE QUESTIONS
QUESTION 1 • BASIC
A can do a work in 20 days and B in 30 days. Find combined time.
Shortcut: (20 × 30) / (20 + 30) = 600 / 50 = 12 days.
QUESTION 2 • MODERATE
A is 50% more efficient than B. If B takes 18 days, how long will A take?
Efficiency Ratio (A:B) = 1.5 : 1 = 3 : 2.
Time Ratio (A:B) = 2 : 3.
Since 3 parts = 18 days, 1 part = 6 days. A takes 2 parts = 12 days.
Time Ratio (A:B) = 2 : 3.
Since 3 parts = 18 days, 1 part = 6 days. A takes 2 parts = 12 days.
❓ FREQUENTLY ASKED QUESTIONS
Q: Why is the LCM method better than fraction addition for Time & Work?
The LCM method converts fractional work into clean integer units (e.g. 60 bricks), eliminating fraction additions and speed-killing decimal errors.
Q: How does the Man-Days formula work?
When workers, days, and hours are involved, Total Work is proportional to (M × D × H). The relationship (M1 × D1 × H1) / W1 = (M2 × D2 × H2) / W2 allows instant solving.