Time and work

⏳ Time & Work – Full explanation

Time and work is a work done by one person or several people It is the math part that calculates how long it will take to finish.

📌 Definition

The time taken to complete a job and the amount of work they do Telling the connectionTime & Workis

🧮 Key Formulas

Work = Time × Efficiency

• ✔ Work
• ✔ Time
• ✔ Efficiency

💡 Basic concept

• ✔ If one completes a piece of work in 10 days → 1 day's work = 1/10
• ✔ If one completes a work in 5 days → 1 day work = 1/5

📊 Example

• ✔ A completes a work in 10 days
• ✔ B completes a work in 20 days

A day's work = 1/10 B one day's work = 1/20

One day's work of A + B = 1/10 + 1/20 = 3/20

Full work = 1 Hence, days = 20/3 ≈ 6.67 days

🔄 Key concepts

• ✔ More work → More time
• ✔ More capacity → less time
• ✔ If many people work together → speed increases

📏 Important notes

• ✔ Work can always be taken as 1
• ✔ Time and Efficiency are inverse of each other.
• ✔ Easy to calculate using LCM method

In the tests “In how many days will A and B together complete the work?”, "How long does it take for someone to quit a job?" Such questions are frequently asked.

⏳ Time & Work – Key formulas

🧮 1. Work base formula

Work = Time × Efficiency

🧮 2. One day work

1 day's work = 1 / days

🧮 3. Working together (A + B)

1 / T = 1 / A + 1 / B

🧮 4. Teamwork (A + B + C)

1 / T = 1 / A + 1 / B + 1 / C

5. Efficiency

Efficiency ∝ 1 / Time

🧮 6. Work rate

Work Ratio = Efficiency Ratio

🧮 7. Man & Days interaction

M₁ × D₁ = M₂ × D₂

📌 Important Notes (TNPSC)

• ✔ Work can always be taken as 1 unit
• ✔ Speedy person → completes work quickly
• ✔ Time and Efficiency inverse
• ✔ Easy if you use LCM method
• ✔ Fraction calculation is important

⏳ Time & Work – 10 Examples + Shortcut Tricks

📘 Example 1

A completes a piece of work in 10 days. B will finish in 20 days. How many days together?

Shortcut:(A × B) / (A + B)

= (10 × 20) / (10 + 20) = 200 / 30 =6⅔ days

📘 Example 2

A – 5 days, B – 10 days

= (5 × 10) / (5 + 10) = 50 / 15 =3⅓ days

📘 Example 3

A – 12 days, B – 18 days

= (12 × 18) / (12 + 18) = 216 / 30 =7.2 days

📘 Example 4

A – 8 days, B – 16 days

= (8 × 16) / (8 + 16) = 128 / 24 =5⅓ days

📘 Example 5

A – 6 days, B – 3 days

= (6 × 3) / (6 + 3) = 18 / 9 =2 days

📘 Example 6

A – 15 days, B – 10 days

= (15 × 10) / (15 + 10) = 150 / 25 =6 days

📘 Example 7

A – 20 days, B – 30 days

= (20 × 30) / (20 + 30) = 600 / 50 =12 days

📘 Example 8

A – 4 days, B – 6 days

= (4 × 6) / (4 + 6) = 24 / 10 =2.4 days

📘 Example 9

A – 9 days, B – 18 days

= (9 × 18) / (9 + 18) = 162 / 27 =6 days

📘 Example 10

A – 7 days, B – 14 days

= (7 × 14) / (7 + 14) = 98 / 21 =4⅔ days

🚀 Key Shortcut Tricks

• ✔ If there are 2 → (A × B) / (A + B)
• ✔ One is fast → his day will be short
• ✔ If Ratio question appears → Use Efficiency
• ✔ If you take LCM, calculation is easy
• ✔ If you know how to convert fractions, you can solve them quickly

🚰 Pipes & Cisterns – Full Description

Pipes & Cisterns refers to pipes that fill or empty a tank A part of mathematics that calculates time using velocity.

📌 Definition

Keep the speed at which a faucet fills or empties the tank Calculating how long it takes for the entire tank to fill or emptyPipes & Cisternsis

🧮 Key Formulas

1️⃣ Filling tube

1 hour of work = 1 / time

2️⃣ Drain pipe

1 hour of work = -1 / time

3️⃣ Work together

1 / T = 1 / A + 1 / B

4️⃣ Fill + Empty

1 / T = 1 / A - 1 / B

💡 Basic concept

• ✔ Filling tube → Positive (+)
• ✔ Drain tube → Negative (-)
• ✔ More speed → less time

📊 Example

• ✔ A pipe → fills in 10 hours
• ✔ B tube → empties in 20 hours

A = 1/10 B = -1/20

Add = 1/10 - 1/20 = 1/20

T = 20 hours

🔄 Key concepts

• ✔ Fill → Plus (+)
• ✔ Empty → Minus (-)
• ✔ Easy if you use LCM method

📏 Important notes

• ✔ Full tank = 1 unit
• ✔ Take work = Fraction
• ✔ Multiple pipes → addition / subtraction

Questions include “If one pipe fills while another pipe empties?”, "How long are two pipes together?" Such questions are frequently asked.