⏱️ Time and Work – SSC Cheat Sheet
🔢 Basic Formulas
- Work = Time × Rate
- Rate = Work / Time
- Time = Work / Rate
- If A can do a work in x days, then A’s 1 day work = 1/x
- If A is x times as efficient as B,
➤ A will take 1/x the time B takes
➤ Work ratio: A : B = x : 1
🧠 Key Concepts & Tricks
✅ 1. One Day Work Method
- If A can do a work in 10 days → A’s 1 day work = 1/10
- A and B together: A’s 1 day + B’s 1 day
✅ 2. LCM Method
Use when multiple people work different days. Take total work as LCM of days.
✅ 3. Efficiency Method
- A does work in 10 days → Efficiency = 100/10 = 10 units/day
- More efficient = More work/day = Less time
🧠 Shortcut Table
| Days Taken | Efficiency |
|---|---|
| 10 | 10 |
| 5 | 20 |
| 20 | 5 |
| 25 | 4 |
💡 Important Cases
🔹 Case 1: A and B together can do a work in X days, B alone in Y days. Find A's days:
- A = (XY) / (Y - X)
🔹 Case 2: A is x% more efficient than B
- Efficiency Ratio = (100 + x) : 100
- Time Ratio = inverse of efficiency
🔹 Case 3: Pipes & Cisterns (same logic):
- Inlet adds work (positive rate)
- Outlet removes work (negative rate)
📘 SSC Previous Year Questions
🔹 Question 1 (SSC CGL 2022)
A can do a piece of work in 12 days. B is 50% more efficient than A. In how many days can B do it?
Solution:
A’s efficiency = 1/12
B is 50% more efficient → Efficiency = 1/12 × 150% = 1/8
So B takes 8 days ✅
🔹 Question 2 (SSC CHSL 2021)
A and B can complete a task in 10 days, B alone in 15 days. In how many days can A alone complete it?
Solution:
A + B = 1/10/day
B = 1/15/day
A = 1/10 – 1/15 = (3 – 2)/30 = 1/30 → A takes 30 days ✅
🔹 Question 3 (SSC MTS 2020)
A, B, and C can complete work in 20, 30, and 60 days respectively. In how many days can they complete the work together?
LCM = 60 units
A: 3 units/day
B: 2 units/day
C: 1 unit/day
Total = 6 units/day → 60/6 = 10 days ✅
🚀 Practice Tricks
- LCM of time values helps convert to total work easily.
- Compare efficiencies by inversing time
- For "leaves after X days" type questions, calculate work done till they leave and who’s left.
🧠 Quick Practice Set
A and B can do work in 12 days, B alone in 18 days. A alone? 👉 A = (12 × 18) / (18 – 12) = 36 days
A completes a job in 8 days, B in 24 days. Together? 👉 1/8 + 1/24 = 1/6 → 6 days
A does half the work in 10 days. Full work? 👉 10 × 2 = 20 days
🔁 Efficiency Conversion Table
| Efficiency | Days |
|---|---|
| 1 | 100 |
| 2 | 50 |
| 4 | 25 |
| 5 | 20 |
| 10 | 10 |