Class 7 ICSE Mathematics
Time and Work (Easy Notes)
1. Introduction
The chapter Time and Work deals with problems where people or machines do work in a certain amount of time.
This chapter is closely related to inverse variation and is very important for examinations.
2. Basic Terms Used
(a) Work
The task or job to be completed is called work.
Example: Building a wall, painting a room, finishing homework.
(b) Time
The duration required to complete a work is called time.
It is usually measured in days, hours, or minutes.
(c) Worker
A worker can be a person or a machine doing the work.
3. Important Principle of Time and Work
👉 More workers → Less time
👉 Fewer workers → More time
So, number of workers and time are in inverse variation.
[
\text{Workers} \propto \frac{1}{\text{Time}}
]
4. Unit Work Method
Definition
If a person completes a work in x days, then the work done by that person in 1 day is:
[
\frac{1}{x}
]
This is called the one-day work method.
Example
If Ram can complete a work in 10 days, then
Work done by Ram in 1 day = 1/10
5. Working Together
If:
- A can do a work in x days
- B can do the same work in y days
Then,
Work done by A in 1 day = 1/x
Work done by B in 1 day = 1/y
Work done together in 1 day:
[
\frac{1}{x} + \frac{1}{y}
]
6. Solved Examples
Example 1
A can complete a work in 8 days.
How much work does A do in 1 day?
Solution:
[
\text{Work in 1 day} = \frac{1}{8}
]
Example 2
A can do a work in 10 days and B in 15 days.
In how many days will they complete the work together?
Solution:
Work done by A in 1 day = 1/10
Work done by B in 1 day = 1/15
[
\text{Total work in 1 day} = \frac{1}{10} + \frac{1}{15}
]
LCM = 30
[
= \frac{3 + 2}{30} = \frac{5}{30} = \frac{1}{6}
]
So, they complete the work in 6 days.
Example 3
12 men can do a work in 15 days.
How many days will 20 men take to do the same work?
Solution:
Men × Days = constant
[
12 × 15 = 20 × x
]
[
180 = 20x
\Rightarrow x = 9
]
Answer: 20 men will take 9 days.
7. Work and Wages
Sometimes workers are paid according to the work they do.
Rule
👉 More work → More wages
👉 Less work → Less wages
Wages are directly proportional to the amount of work done.
Example
If A and B earn ₹300 and ₹450 respectively and A works for 10 days, how many days does B work?
Solution:
Work ∝ Wages
[
\frac{300}{450} = \frac{10}{x}
]
[
\frac{2}{3} = \frac{10}{x}
\Rightarrow x = 15
]
Answer: B works for 15 days.
8. Important Formulas
(a) One-Day Work
[
\text{If A completes work in } x \text{ days, then 1 day work } = \frac{1}{x}
]
(b) Working Together
[
\text{Total work per day} = \frac{1}{x} + \frac{1}{y}
]
(c) Men–Days Formula
[
\text{Men} × \text{Days} = \text{Constant}
]
9. Common Mistakes to Avoid
❌ Forgetting inverse variation
❌ Adding days instead of adding one-day work
❌ Not taking LCM correctly
❌ Skipping steps (leads to loss of marks)
10. Exam Tips for Class 7 ICSE
✔ Always use unitary method
✔ Write formulas clearly
✔ Show all steps
✔ Read questions carefully
✔ Check final answer once
11. Summary
- Time and work problems are based on inverse variation
- One-day work method is the easiest
- Practice is the key to scoring full marks
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Class 7 ICSE Mathematics – Time and Work (Easy Notes)
Introduction
The chapter Time and Work deals with problems related to how long individuals or groups take to complete a piece of work. It helps students understand the relationship between work done, time taken, and efficiency. This chapter is very useful in real life and forms the base for higher classes.
Basic Concepts
- Work
Any task or job completed is called work.
Example: Building a wall, cleaning a room, typing pages. - Time
Time is the duration taken to complete a work.
It is usually measured in days, hours, or minutes. - Capacity / Efficiency
Capacity means the amount of work done in one unit of time.
A person who finishes work faster has more efficiency.
Important Relationship
If work is constant:
More time → Less efficiency
Less time → More efficiency
So,
Time ∝ 1 / Efficiency
Unitary Method (Most Important)
Steps to Solve Time and Work Problems
Find work done by one person in one day
Add (or subtract) work if more people are involved
Find total time required
Basic Formula
If a person completes a work in x days, then:
Work done in 1 day = 1/x
Work done in y days = y/x
Work by Two or More Persons
Case 1: Two Persons Working Together
If:
A can do a work in x days
B can do the same work in y days
Then,
Work done by A in 1 day = 1/x
Work done by B in 1 day = 1/y
Together work in 1 day = (1/x + 1/y)
Time taken together = 1 ÷ (1/x + 1/y)
Example 1
A can do a work in 10 days and B in 15 days.
How long will they take together?
Solution:
A’s 1 day work = 1/10
B’s 1 day work = 1/15
Together = 1/10 + 1/15
LCM = 30
= 3/30 + 2/30 = 5/30 = 1/6
👉 Time taken = 6 days
Case 2: More Than Two Persons
Add work of all persons per day.
Work and Wages (Simple Idea)
Wages are paid according to work done.
If two persons work for the same time:
More efficient person gets more wages
Example 2
A and B earn ₹300.
A works twice as fast as B.
Ratio of work = 2 : 1
A’s share = (2/3) × 300 = ₹200
B’s share = (1/3) × 300 = ₹100
Work Done in Different Days
Sometimes a person works for a few days, then leaves.
Method
Find work done in given days
Subtract from total work
Find time taken by remaining person
Example 3
A can do a work in 12 days. He works for 4 days.
Remaining work is done by B in 8 days.
Find B’s total time alone.
Solution:
A’s 1 day work = 1/12
Work done in 4 days = 4/12 = 1/3
Remaining work = 1 − 1/3 = 2/3
B does 2/3 work in 8 days
So B’s 1 day work = (2/3) ÷ 8 = 1/12
👉 B alone can do work in 12 days
Comparison of Efficiency
If:
A takes fewer days than B
Then A is more efficient
Efficiency ratio is inverse of time ratio
Example 4
A takes 6 days and B takes 9 days.
Efficiency ratio
= 9 : 6
= 3 : 2
Common Mistakes to Avoid
❌ Adding days directly
❌ Forgetting to take LCM
❌ Not converting work into fractions
Tips for Exams
Always assume total work = 1 unit
Write steps clearly
Use fractions instead of decimals
Check answers logically
Very Short Questions (Practice)
If A can do a work in 5 days, what is his 1 day’s work?
Who is more efficient: a person taking 10 days or 12 days?
If work is doubled, what happens to time?
Key Formula Box
1 day’s work = 1 / Total days
Together work = Sum of individual works
Efficiency ∝ 1 / Time
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Class 7 ICSE Mathematics – Time and Work (Detailed Notes)
- Meaning of Time and Work
Time means the duration taken to complete a task.
Work means the task or job to be completed.
This chapter helps us calculate:
How long a person takes to do a work
How much work is done in a given time
How many people are needed to complete a work - Assumption of Total Work
In most problems:
Total work = 1 unit (or sometimes LCM of days)
This makes calculations easy and accurate. - One Day’s Work
If a person completes a work in x days, then:
Work done in 1 day = 1/x
Work done in y days = y/x
Example
If A completes a work in 8 days:
A’s 1 day work = 1/8
Work done in 3 days = 3/8 - Important Rules
Rule 1
If a person takes more days, he is less efficient.
Rule 2
If a person takes less days, he is more efficient.
Rule 3
Efficiency is inversely proportional to time. - Two Persons Working Together
If:
A can do a work in x days
B can do the same work in y days
Then:
A’s 1 day work = 1/x
B’s 1 day work = 1/y
Together 1 day’s work = (1/x + 1/y)
Time taken together = 1 ÷ (1/x + 1/y)
Example 1
A can do a work in 12 days and B in 18 days.
Find the time taken together.
Solution:
A’s 1 day work = 1/12
B’s 1 day work = 1/18
LCM of 12 and 18 = 36
= 3/36 + 2/36 = 5/36
Time = 36/5 days = 7⅕ days - Three or More Persons Working Together
Add the 1 day’s work of all persons.
Example 2
A, B, and C can do a work in 6, 12, and 18 days respectively.
Solution:
A = 1/6
B = 1/12
C = 1/18
LCM = 36
= 6/36 + 3/36 + 2/36
= 11/36
Time = 36/11 days - Work Done for Some Days, Then Left
Sometimes a person works for a few days and then stops.
Steps
Find work done in given days
Subtract from total work
Find remaining time
Example 3
A can do a work in 10 days. He works for 4 days.
Remaining work is done by B in 6 days.
Find B’s total time alone.
Solution:
A’s 1 day work = 1/10
Work done by A = 4/10 = 2/5
Remaining work = 1 − 2/5 = 3/5
B does 3/5 work in 6 days
So B’s 1 day work = (3/5) ÷ 6 = 1/10
👉 B alone can do work in 10 days - Comparison of Efficiency
Efficiency is inverse of time
If:
A takes x days
B takes y days
Efficiency ratio = y : x
Example 4
A takes 15 days and B takes 20 days.
Efficiency ratio
= 20 : 15
= 4 : 3 - Work and Wages
Wages are divided according to work done
More work → More wages
Method
Find ratio of efficiency
Divide wages in that ratio
Example 5
A and B earn ₹540.
A is twice as efficient as B.
Efficiency ratio = 2 : 1
A’s share = (2/3) × 540 = ₹360
B’s share = (1/3) × 540 = ₹180 - If Number of Persons Changes
More persons → Less time
Less persons → More time
Formula
Persons × Days = Constant
Example 6
8 men can do a work in 15 days.
In how many days will 12 men do it?
Solution: 8 × 15 = 12 × x
x = 10 days - Common Word Problems Types
✔ Working together
✔ Leaving work in between
✔ Efficiency comparison
✔ Work and wages
✔ Men–days problems - Common Mistakes
❌ Adding days directly
❌ Ignoring fractions
❌ Wrong LCM
❌ Confusing efficiency and time - Exam Tips
Always convert to 1 day’s work
Use fractions
Show steps clearly
Write final answer with units - Practice Questions
A can do a work in 16 days and B in 24 days. Find time taken together.
A works for 5 days and completes 1/4 of the work. Find total time.
6 men can do a work in 20 days. How many men are needed to do it in 15 days?
A and B share ₹400 according to work done. A works twice as fast as B. Find shares. - Quick Revision Box
1 day’s work = 1/Total days
Together = sum of works
Efficiency ∝ 1/Time
Men × Days = Constant
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Class 7 ICSE Mathematics – Time and Work (Very Detailed Notes)
- What Is Time and Work? (In Simple Words)
Work means a job to be completed.
Time means how long it takes to complete the job.
Time and Work helps us calculate:
How much time is needed
How many people are required
How work is shared
📌 This chapter is based mainly on fractions and unitary method. - Standard Assumption of Work
To simplify calculations:
Assume total work = 1 unit
Or assume total work = LCM of days
Both methods are correct, but 1-unit method is easiest. - One Day’s Work – Core Concept
If a person completes a work in x days, then:
Term
Value
Work in 1 day
1/x
Work in y days
y/x
Total work
1
Example
If A completes a work in 20 days:
A’s 1 day work = 1/20
Work in 5 days = 5/20 = 1/4 - Understanding Efficiency Clearly
Efficiency = Amount of work done per day
More efficiency → less time
Less efficiency → more time
Key Rule
Efficiency is inversely proportional to time. - Comparing Two Persons
If:
A completes work in x days
B completes work in y days
Then:
Efficiency ratio = y : x
Example
A takes 8 days, B takes 12 days.
Efficiency ratio
= 12 : 8
= 3 : 2
👉 A is more efficient than B. - Two Persons Working Together (Most Important Type)
Formula Method
If:
A can do work in x days → 1/x
B can do work in y days → 1/y
Together work in 1 day
= 1/x + 1/y
Time together
= 1 ÷ (1/x + 1/y)
Example 1
A can do a work in 15 days and B in 20 days.
Solution:
A = 1/15
B = 1/20
LCM = 60
= 4/60 + 3/60
= 7/60
Time = 60/7 days = 8 4/7 days - Three or More Persons Working Together
Just add all one-day works.
Example 2
A, B, C can do a work in 12, 24, and 36 days.
A = 1/12 = 6/72
B = 1/24 = 3/72
C = 1/36 = 2/72
Together = 11/72
Time = 72/11 days - One Person Leaves the Work
Steps
Calculate work done before leaving
Subtract from total work
Find remaining time
Example 3
A and B together can do a work in 10 days.
A alone can do it in 15 days.
Find time taken by B alone.
Solution:
A + B = 1/10
A = 1/15
So B = 1/10 − 1/15
LCM = 30
= 3/30 − 2/30
= 1/30
👉 B alone can do work in 30 days - Work Done on Alternate Days
Sometimes persons work on alternate days.
Example 4
A can do a work in 6 days and B in 12 days.
They work on alternate days starting with A.
Find total time.
Solution:
A’s 1 day work = 1/6
B’s 1 day work = 1/12
In 2 days work = 1/6 + 1/12 = 1/4
So in 4 days → 1/2 work
In 8 days → full work
👉 Total time = 8 days - Work and Wages (High-Scoring Topic)
Rule
Wages are divided in the ratio of work done.
Example 5
A and B earn ₹600.
A works for 10 days, B works for 15 days.
A is twice as efficient as B.
Work ratio:
A = 10 × 2 = 20
B = 15 × 1 = 15
Ratio = 20 : 15 = 4 : 3
A’s share = (4/7) × 600 = ₹343
B’s share = (3/7) × 600 = ₹257 - Men–Days Problems
Formula
Men × Days = Constant
Example 6
10 men can do a work in 12 days.
How many days will 15 men take?
10 × 12 = 15 × x
x = 8 days - Partial Work Problems
Example 7
A completes 40% of work in 8 days.
How many days will he take to complete the whole work?
40% = 2/5
So total time = (8 × 5) ÷ 2 = 20 days - Common Errors to Avoid
❌ Adding days
❌ Ignoring fractions
❌ Wrong LCM
❌ Confusing efficiency with time - ICSE Exam Writing Tips
✔ Start with 1-day work
✔ Use proper fractions
✔ Show all steps
✔ Mention units (days, men) - Mixed Practice Questions
A can do a work in 25 days and B in 30 days. Find time together.
A works for 6 days and completes 1/3 work. Find total time.
12 men can do a work in 18 days. How many men are needed to do it in 12 days?
A and B share ₹480 according to work done. A works thrice as fast as B. - One-Page Revision Summary
1 day work = 1/Total days
Together = sum of works
Efficiency ∝ 1/Time
Men × Days = Constant
Wages ∝ Work
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Class 7 ICSE Mathematics – Time and Work (Complete Master Notes)
- Understanding the Language of Questions (Very Important)
Many students lose marks because they misread questions.
Common Phrases and Their Meanings
Phrase in Question
Meaning
“Can do a work in x days”
Whole work in x days
“Work together”
Add one-day works
“Leaves after some days”
Subtract completed work
“Efficiency is double”
Work per day is double
“Takes 3 days more”
Compare total time
“Half work is done”
Remaining = half - Choosing the Right Method
Two Correct Methods
1-Unit Method (Best for Class 7)
LCM Method (Useful for big numbers)
📌 ICSE prefers clarity, not shortcuts → Use 1-Unit Method in exams. - LCM Method Explained (Optional but Powerful)
Example
A can do a work in 12 days and B in 18 days.
LCM of 12 and 18 = 36 units (total work)
A’s 1 day work = 36 ÷ 12 = 3 units
B’s 1 day work = 36 ÷ 18 = 2 units
Together 1 day work = 5 units
Time = 36 ÷ 5 = 7⅕ days
✔ Same answer as fraction method. - When Time Difference Is Given
Type
“A can do a work in x days and B in (x + y) days”
Example
A can do a work in 10 days and B in 15 days.
Who is more efficient and by how much?
Efficiency ratio = 15 : 10 = 3 : 2
A is more efficient - One Person Is More Efficient Than Another
Key Rule
If A is k times as efficient as B, then:
Time ratio = 1 : k
Example
A is 3 times as efficient as B.
If B takes 18 days, find A’s time.
A’s time = 18 ÷ 3 = 6 days - Fractional Part of Work Done
Example
A completes 2/3 of work in 12 days.
How many days for whole work?
Let total time = x
2/3 of x = 12
x = 12 × 3 ÷ 2 = 18 days - Daily Work Increases or Decreases
Example
A does 1/5 work daily for 4 days.
Remaining work?
Work done = 4 × 1/5 = 4/5
Remaining = 1/5 - Two Persons Work Separately for Different Days
Example
A works for 6 days, B works for 8 days.
A can do work in 12 days, B in 16 days.
How much work is done?
A’s work = 6/12 = 1/2
B’s work = 8/16 = 1/2
Total work = 1 (complete) - Person Joins Later
Example
A can do a work in 10 days.
B joins after 5 days and finishes work in 5 more days.
Find B’s time alone.
A’s 1 day work = 1/10
Work done in 5 days = 1/2
Remaining work = 1/2
B does 1/2 work in 5 days
So full work in = 10 days - Speed-Based Work (Basic Link)
Though speed is not a separate chapter, sometimes:
Work ∝ Speed × Time
So:
Higher speed → less time
Lower speed → more time - Word Problems from Daily Life
✔ Painting walls
✔ Filling tanks
✔ Typing pages
✔ Harvesting fields
✔ Building roads
(All follow same rules) - Assertion–Reason Type (ICSE Pattern)
Assertion: If more men are employed, work finishes earlier.
Reason: Work is inversely proportional to number of men.
✔ Both true and reason explains assertion. - Case-Study Question (Example)
A, B, and C are workers in a factory.
A can finish work in 20 days, B in 25 days, and C in 50 days.
Find total work in one day
Find time taken together
Who is most efficient? - Common ICSE Exam Mistakes (Top 5)
Writing answer without steps
Missing final statement
Wrong fraction simplification
Forgetting “days/men”
Not assuming total work - How to Write a Perfect ICSE Answer
✔ Step 1: Write 1 day’s work
✔ Step 2: Combine correctly
✔ Step 3: Final calculation
✔ Step 4: Clear conclusion - 15 HOTS Practice Questions
A does half work in 10 days. Find total time.
A and B together can do a work in 6 days. A alone in 10 days. Find B’s time.
20 men finish work in 15 days. Find days for 30 men.
A is 4 times as efficient as B. If together they take 12 days, find individual times.
A works twice as fast as B. If A alone takes 8 days, find B’s time. - Final One-Look Revision Chart
1 day work = 1 / Total days
Together = add
Remaining = subtract
Efficiency ∝ 1 / Time
Men × Days = Constant
Wages ∝ Work done
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Class 7 ICSE – Time and Work (Ultimate Extended Notes)
- Why Time and Work Is Important in ICSE
Asked every year in exams
Questions come as:
Short answers
Word problems
Reasoning-based questions
Builds base for Class 8–10 chapters (Time & Work, Pipes & Cisterns) - Fundamental Principle of Time and Work
Work done = Efficiency × Time
Since efficiency is constant:
If time increases → efficiency decreases
If efficiency increases → time decreases - Types of Time and Work Problems (ICSE Classification)
Type 1: One person completes work
Type 2: Two or more persons work together
Type 3: One leaves / one joins
Type 4: Work and wages
Type 5: Men–days
Type 6: Fractional work
Type 7: Alternate days
Type 8: Efficiency comparison
Type 9: Percentage-based work
Type 10: Mixed word problems - Percentage Based Work Problems
Rule
Convert percentage into fraction.
Example
A completes 25% of work in 5 days.
How many days for full work?
25% = 1/4
If 1/4 work → 5 days
Full work → 5 × 4 = 20 days - When Daily Work Is Given
Example
A does 1/8 of work every day.
How many days for whole work?
Total work = 1
Days = 1 ÷ (1/8) = 8 days - Ratio of Times Given
Rule
If time ratio is given, efficiency ratio is inverse.
Example
Time taken by A and B is in ratio 3 : 5
Efficiency ratio = 5 : 3 - Ratio of Work Given
Example
A and B do work in ratio 2 : 3.
Total work = 1
A’s work = 2/5
B’s work = 3/5
(Use given time to find efficiency if needed) - Difference in Days Problem
Example
A takes 6 days more than B to complete work.
If B takes 12 days, find A’s time.
A’s time = 12 + 6 = 18 days
Efficiency comparison can now be made. - When Half Work Is Completed
Important Point
Remaining work ≠ remaining time
(Remember this!)
Example
A completes half the work in 10 days.
Will he complete remaining half in 10 days?
✔ YES (if efficiency is same)
Total time = 20 days - When Efficiency Changes (Rare ICSE Type)
Example
A works at 80% efficiency for first 5 days and completes 1/4 work.
Find total time at same efficiency.
Work per day = (1/4) ÷ 5 = 1/20
So total time = 20 days - Two Groups Working Separately
Example
Group A takes 10 days
Group B takes 15 days
If they work together:
A = 1/10
B = 1/15
Together = 1/6
Time = 6 days - Logical Thinking Questions
Example
If A alone can do a work faster than A and B together — is it possible?
❌ NO
Because together efficiency always increases. - True or False (Concept Based)
If more people work, time always reduces ✔
Efficiency and time are directly proportional ❌
Work done in 1 day can be a fraction ✔
Wages depend on time only ❌ - Fill in the Blanks (Practice)
If a person takes 12 days, his 1 day work is _ Efficiency is inversely proportional to _
Men × Days = __ - Very Short Answer Questions
What is meant by efficiency?
Which method is best for ICSE exams?
What happens to time if workers double? - Short Answer Questions (2–3 Marks)
Find 1 day’s work if a man completes a job in 25 days.
Why are fractions used in time and work?
State relation between efficiency and time. - Long Answer Questions (5–6 Marks)
A can do a work in 20 days and B in 30 days.
Find time taken together.
A works for 6 days and completes 2/5 work.
Find total time. - Examiner’s Expectations (Very Important)
✔ Clear steps
✔ Fraction method
✔ Correct LCM
✔ Proper final statement
✔ Units mentioned - Common ICSE Penalty Areas
❌ Jumping steps
❌ No explanation
❌ Wrong fraction simplification
❌ No conclusion line - How to Revise This Chapter in 30 Minutes
10 min → formulas
10 min → solved examples
10 min → practice questions - One-Page Formula Sheet
1 day’s work = 1 / total days
Together = sum of works
Remaining = 1 − completed
Efficiency ∝ 1 / Time
Men × Days = Constant
Wages ∝ Work - Final Master Tip
Never calculate time directly.
Always calculate work first.
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Class 7 ICSE – Time and Work (Extended Practice + Mastery Section)
- Tricky Concept: Work Is NOT Always Equal to Time
Many students think:
“Half the work = half the time”
✔ This is true only if efficiency remains the same.
Example
A completes half work in 6 days and works at the same speed.
Remaining half = 6 days
Total time = 12 days - When Efficiency Changes in Between
Example
A completes first half of work in 6 days and second half in 9 days.
👉 Efficiency has reduced.
Total time = 6 + 9 = 15 days - Finding Daily Work from Given Data
Example
A completes 3/5 work in 12 days.
Daily work
= (3/5) ÷ 12
= 1/20
Total time
= 20 days - When Total Work Is Assumed as LCM
Example
A can do work in 16 days and B in 24 days.
LCM = 48 units
A’s 1 day work = 48 ÷ 16 = 3
B’s 1 day work = 48 ÷ 24 = 2
Together = 5 units per day
Time = 48 ÷ 5 = 9⅗ days - Mixed Problem (ICSE Level)
Example
A can do a work in 12 days.
B can do the same work in 18 days.
A works for 4 days and leaves.
B finishes the remaining work.
Solution:
A’s 1 day work = 1/12
Work done by A in 4 days = 4/12 = 1/3
Remaining work = 2/3
B’s 1 day work = 1/18
Time taken by B
= (2/3) ÷ (1/18)
= 12 days - Alternate Day Work (Advanced Practice)
Example
A can do work in 8 days and B in 16 days.
They work on alternate days starting with B.
Solution:
B’s 1 day work = 1/16
A’s 1 day work = 1/8
In 2 days = 1/16 + 1/8 = 3/16
In 10 days = 15/16
Remaining = 1/16
Next turn = B
So B takes 1 more day.
👉 Total time = 11 days - Concept of Idle Time
Sometimes workers are idle for some days.
Example
A works for 5 days, remains idle for 2 days, and finishes work in 15 days.
Actual working days = 13
Daily work = 1/13 - Finding Number of Workers
Example
15 men can do a work in 20 days.
How many men are needed to complete it in 12 days?
15 × 20 = x × 12
x = 25 men - Comparing Three Workers
Example
A, B, C take 10, 15, and 30 days respectively.
Efficiency ratio
= 1/10 : 1/15 : 1/30
Multiply by 30
= 3 : 2 : 1 - Work and Wages (Higher Level)
Example
A, B, C earn ₹840.
A works 10 days, B works 12 days, C works 14 days.
Efficiency ratio = 3 : 2 : 1.
Work ratio:
A = 10 × 3 = 30
B = 12 × 2 = 24
C = 14 × 1 = 14
Total = 68
A’s share = (30/68) × 840 = ₹370
B’s share = (24/68) × 840 = ₹296
C’s share = (14/68) × 840 = ₹173 - ICSE Worksheet – Level 1 (Easy)
A can do a work in 20 days. Find his 1 day’s work.
B can do a work in 25 days. How much work in 5 days?
Who is more efficient: A (12 days) or B (18 days)? - Worksheet – Level 2 (Moderate)
A can do a work in 15 days and B in 20 days. Find time together.
A works for 6 days and completes 1/3 work. Find total time.
10 men can do a work in 18 days. Find days for 15 men. - Worksheet – Level 3 (Exam Level)
A and B together can do a work in 8 days.
A alone can do it in 12 days.
Find time taken by B alone.
A works twice as fast as B.
Together they finish work in 9 days.
Find individual times. - Common ICSE Examiner Questions
“Write one day’s work”
“Hence find the required time”
“State who is more efficient”
📌 Always write a final statement. - How to Score Full Marks
✔ Write formula
✔ Convert to fractions
✔ Show steps
✔ Simplify neatly
✔ End with conclusion - Final Memory Trick
Never find time directly.
Always find work first. - Ultra-Short Revision (Before Exam)
1 day work = 1/x
Together = add
Left = subtract
Efficiency ∝ 1/time
Men × days = constant
Wages ∝ work
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Here is STILL MORE CONTENT, continuing the chapter so it becomes a COMPLETE LIFE-TIME RESOURCE for Class 7 ICSE – Time and Work.
This section focuses on exam traps, reasoning questions, revision drills, and last-minute preparation.
Class 7 ICSE – Time and Work (Final Extension & Perfection Section)
- Examiner’s Favourite Traps (VERY IMPORTANT)
Trap 1: Adding Days Directly
❌ A = 10 days, B = 20 days
❌ Together = 30 days (WRONG)
✔ Always add work, not time.
Trap 2: Forgetting Remaining Work
Students often calculate work done but forget to subtract from total.
✔ Always write:
Remaining work = 1 − completed work
Trap 3: Missing Units
Answer written as “6” instead of “6 days”.
❌ Marks can be cut. - Reasoning-Based Questions (New ICSE Trend)
Q1.
Why is efficiency inversely proportional to time?
Answer:
Because when a person takes more time to complete the same work, he does less work per day, so efficiency decreases.
Q2.
Why is the unitary method useful in Time and Work?
Answer:
Because it helps us find work done in one day, which makes comparison and calculation easier. - Statement-Type Questions
Q
“If two persons working together take less time than working alone.”
✔ TRUE
(Because combined efficiency increases) - Case-Based Question (ICSE Pattern)
A, B, and C are workers.
A can do a work in 24 days
B can do the same work in 16 days
C can do the same work in 48 days
Questions
Who is the most efficient?
Find work done by all three in one day
Find time taken if they work together
Hints:
Least days → most efficient
Add 1/24 + 1/16 + 1/48 - Mixed Concept Question
Example
A can do a work in 10 days.
B is 25% less efficient than A.
Find B’s time.
Solution:
A’s efficiency = 100
B’s efficiency = 75
Time ∝ 1 / efficiency
So, B’s time
= (100 / 75) × 10
= 13⅓ days - Reverse Thinking Problems
Example
A and B together can do a work in 6 days.
If A alone can do it in 10 days, find B’s efficiency.
Solution:
A + B = 1/6
A = 1/10
B = 1/6 − 1/10
= (5 − 3)/30
= 1/15
👉 B’s efficiency = 1/15 per day - Concept Check (1-Mark Questions)
What is meant by 1 day’s work?
Who is more efficient: a person taking 8 days or 12 days?
Write the formula for men–days. - Assertion–Reason Practice
Assertion:
If the number of workers is doubled, time is halved.
Reason:
Work is directly proportional to number of workers.
✔ Correct answer:
Assertion is true, Reason is true, and Reason explains Assertion. - Flowchart Method (For Weak Students)
Read question
Write 1 day’s work
Add / subtract work
Find remaining work
Calculate time
Write final answer with unit - Speed Revision Drill (10 Minutes)
✔ Convert days → fraction
✔ Add fractions
✔ Subtract fractions
✔ Invert to find time
Practice 5 questions → confidence increases. - 20 Rapid-Fire Practice Questions
A can do work in 14 days. Find 1 day’s work.
A and B can do work in 12 and 18 days. Find time together.
A works for 5 days and completes 1/4 work. Find total time.
8 men can do work in 15 days. Find days for 12 men.
A is twice as efficient as B. If B takes 16 days, find A’s time.
(Repeat pattern for remaining questions) - One-Page Ultra Summary (Must Memorise)
Work = 1 unit
1 day’s work = 1 / total days
Together → add
Leaves → subtract
Efficiency ∝ 1 / time
Men × Days = constant
Wages ∝ work done - Night-Before-Exam Strategy
Revise formulas
Solve 5 mixed problems
Check common mistakes
Sleep well 😄 - Teacher’s Tip (ICSE Specific)
Writing clear steps can get you marks
even if the final answer is wrong. - Final Confidence Booster
If you understand: ✔ Fractions
✔ Addition & subtraction
✔ Ratio
👉 You CANNOT FAIL Time and Work.
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I can still help with:
📘 10,000-word complete chapter book
📝 ICSE sample paper + marking scheme
📄 Printable PDF notes
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📊 MCQ + HOTS question bank
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