Time and Work for CUET, CLAT & IPMAT – Complete Guide
Time and Work for CUET, CLAT & IPMAT – Complete Guide with Concepts, Types, Examples & Tricks
Time and Work is one of the most important topics in Quantitative Aptitude for competitive exams like CUET, CLAT, and IPMAT. Every year 1–3 questions are directly or indirectly asked from this chapter.
If you understand the basic concepts, formulas, and shortcut tricks, you can easily solve these questions within seconds.
In this detailed guide, we will cover:
- ✅ Basic Concept of Time and Work
- ✅ Important Formulas
- ✅ Types of Questions
- ✅ Solved Examples with Detailed Explanation
- ✅ Shortcut Tricks for Exams
- ✅ Practice Questions
1️⃣ Basic Concept of Time and Work
The fundamental principle of Time and Work is:
Work = Time × Efficiency
Important Points:
-
If a person completes a work in x days,
then 1 day's work = 1/x -
If A completes a work in 10 days,
then A’s 1-day work = 1/10 -
Efficiency is inversely proportional to time:
If time decreases → efficiency increases
If time increases → efficiency decreases
2️⃣ Important Formulas for Time and Work
✔ Work Formula
Work = Time × Efficiency
✔ Combined Work Formula
If A completes work in x days and B in y days:
✔ Efficiency Ratio
If A takes 10 days and B takes 5 days:
Efficiency ratio = 5 : 10 = 1 : 2
(B is twice as efficient as A)
TYPES OF TIME AND WORK QUESTIONS
🔹 Type 1: Basic Individual Work
Example 1:
A can complete a work in 12 days. In how many days will he complete 50% of the work?
Solution:
1 day work = 1/12
50% work = 1/2
Time = (1/2) ÷ (1/12)
= (1/2) × 12
= 6 days
✅ Answer: 6 days
🔹 Type 2: Two Persons Working Together
Example 2:
A can complete a work in 10 days and B in 15 days. In how many days will they complete the work together?
Solution:
A’s 1-day work = 1/10
B’s 1-day work = 1/15
Total work per day:
= 1/10 + 1/15
LCM = 30
= 3/30 + 2/30
= 5/30
= 1/6
Thus, total time = 6 days
✅ Answer: 6 days
🔹 Type 3: Efficiency Based Questions
Example 3:
A is twice as efficient as B. A completes work in 12 days. In how many days will B complete the work?
Solution:
If A is twice efficient → B is half efficient
If A takes 12 days → B will take 24 days
✅ Answer: 24 days
🔹 Type 4: Work Left / Partial Work
Example 4:
A can complete a work in 8 days. After working for 3 days, how much work is left?
Solution:
1 day work = 1/8
Work done in 3 days = 3/8
Work left = 1 – 3/8
= 5/8
✅ Answer: 5/8 work left
🔹 Type 5: Alternating Work
Example 5:
A can complete work in 10 days and B in 20 days. They work on alternate days starting with A. In how many days will the work be completed?
Solution:
A’s 1-day work = 1/10
B’s 1-day work = 1/20
Work done in 2 days:
= 1/10 + 1/20
LCM = 20
= 2/20 + 1/20
= 3/20
In 2 days → 3/20 work
Now divide:
Total work = 1
1 ÷ (3/20) = 20/3 = 6 cycles (approx)
After 6 cycles (12 days):
Work done = 6 × (3/20) = 18/20
Remaining work = 2/20 = 1/10
Next day is A’s turn:
A does 1/10 in 1 day
Total time = 13 days
✅ Answer: 13 days
🔹 Type 6: Pipes and Cisterns (Important for CUET & IPMAT)
This is similar to Time and Work.
- Filling pipe → Positive work
- Emptying pipe → Negative work
Example 6:
A pipe fills tank in 12 hours and another empties in 18 hours. In how many hours will tank be filled?
Solution:
Filling rate = 1/12
Emptying rate = 1/18
Net rate = 1/12 – 1/18
LCM = 36
= 3/36 – 2/36
= 1/36
Thus tank fills in 36 hours
✅ Answer: 36 hours
🔹 Type 7: Men, Women & Children Efficiency
Sometimes questions involve:
- 2 men = 3 women
- 1 woman = 2 children
Use efficiency conversion method.
Step:
Convert everyone into one unit (men or women or children).
Then apply normal Time and Work formula.
SHORTCUT TRICKS FOR EXAMS
🔥 Trick 1: Use LCM Method
Instead of fractions, assume total work = LCM of days.
Example:
A = 10 days
B = 15 days
LCM = 30
A’s 1 day work = 3 units
B’s 1 day work = 2 units
Together = 5 units per day
Total time = 30/5 = 6 days
Faster and easier!
🔥 Trick 2: Efficiency Direct Method
If A is twice efficient → time becomes half
Efficiency ↑ → Time ↓
IMPORTANT FOR CUET, CLAT & IPMAT
- CUET → Direct formula-based questions
- CLAT → Logical + Time and Work mixture
- IPMAT → Twisted & concept-based questions
Focus more on:
✔ Combined work
✔ Alternating work
✔ Efficiency ratio
✔ Pipes and Cisterns
Practice Questions
- A completes work in 15 days and B in 20 days. Find total time together.
- A is 3 times efficient as B. If B takes 24 days, find A’s time.
- Two pipes fill tank in 8 hrs and 12 hrs. Find total time.
- A completes half work in 5 days. Find total time.
- A and B together complete work in 6 days. A alone in 10 days. Find B’s time.
Final Words
Time and Work is a scoring topic in CUET, CLAT and IPMAT. If you practice 40–50 quality questions and understand efficiency logic properly, you can solve any question within 30 seconds.
👉 Practice regularly
👉 Use LCM method
👉 Avoid lengthy fraction calculations
Important Formulae – Time and Work (CUET | CLAT | IPMAT)
1. Basic Formula
Work = Time × Efficiency
Time = Work ÷ Efficiency
Efficiency = Work ÷ Time
2. Individual Work
If a person completes a work in x days:
1 day work = 1/x
x days work = 1 (complete work)
3. Two Persons Working Together
If A completes work in x days
and B completes work in y days:
1 day combined work = (1/x + 1/y)
Total time taken together = xy / (x + y)
4. Three Persons Working Together
If A, B, C take x, y, z days respectively:
1 day work = (1/x + 1/y + 1/z)
Total time taken together = xyz / (xy + yz + zx)
5. Efficiency and Time Relationship
Efficiency is inversely proportional to Time.
If efficiency ratio of A : B = m : n
Then time ratio of A : B = n : m
6. If One Person is More Efficient
If A is k times as efficient as B:
Time taken by A = (Time of B) ÷ k
Time taken by B = k × (Time of A)
7. Work Done in Given Days
If total work = 1
Work done in t days (when total time is x days) = t/x
Work left = 1 − (t/x)
8. Alternate Day Work
If A and B work on alternate days:
Work done in 2 days = (1/x + 1/y)
Number of cycles = Total work ÷ Work in 2 days
9. Pipes and Cisterns
Filling pipe → Positive work
Emptying pipe → Negative work
Net work per hour = (1/x − 1/y)
Total time = 1 ÷ Net rate
10. LCM Method (Fastest Method for Exams)
Step 1: Take LCM of given days as total work.
Step 2: Calculate 1 day work in units.
Step 3: Add efficiencies.
Step 4: Total time = Total work ÷ Combined efficiency.
🔥 Most Important Exam Formula
If A takes x days and B takes y days:
Time together = xy / (x + y)
📌 Time and Work – MCQs with Answers & Detailed Explanation
(For CUET | CLAT | IPMAT)
🔹 Basic Level
Q1. A can complete a work in 12 days. In how many days will he complete the whole work?
A) 10
B) 12
C) 14
D) 6
Answer: B) 12
Explanation:
Given A completes the entire work in 12 days.
So total time required = 12 days.
Q2. A can complete a work in 15 days. What fraction of work does he complete in 1 day?
A) 1/15
B) 1/5
C) 15
D) 1/30
Answer: A) 1/15
Explanation:
1 day work = 1 / Total days
= 1/15
Q3. A can do a work in 10 days and B in 20 days. In how many days will they complete it together?
A) 5
B) 6⅔
C) 8
D) 4
Answer: B) 6⅔
Explanation:
A’s 1 day work = 1/10
B’s 1 day work = 1/20
Together = 1/10 + 1/20
LCM = 20
= 2/20 + 1/20 = 3/20
Total time = 1 ÷ (3/20)
= 20/3 = 6⅔ days
Q4. A completes a work in 8 days. After working 3 days, how much work is left?
A) 3/8
B) 5/8
C) 1/8
D) 1/2
Answer: B) 5/8
Explanation:
Work done in 3 days = 3/8
Work left = 1 − 3/8
= 5/8
Q5. A is twice as efficient as B. If B takes 24 days, A will take:
A) 48
B) 12
C) 18
D) 6
Answer: B) 12
Explanation:
Efficiency ↑ → Time ↓
If A is twice efficient, time becomes half.
24 ÷ 2 = 12 days
🔹 Moderate Level
Q6. A can do a work in 18 days and B in 12 days. In how many days will they finish the work together?
A) 7.2
B) 8
C) 6
D) 9
Answer: A) 7.2 days
Explanation:
1/18 + 1/12
LCM = 36
= 2/36 + 3/36
= 5/36
Total time = 36/5
= 7.2 days
Q7. A and B together complete work in 6 days. A alone completes it in 15 days. In how many days will B complete the work alone?
A) 10
B) 12
C) 8
D) 9
Answer: A) 10
Explanation:
1/(A+B) = 1/6
1/A = 1/15
1/B = 1/6 − 1/15
LCM = 30
= 5/30 − 2/30
= 3/30 = 1/10
So B alone = 10 days
Q8. If 6 men can do a work in 12 days, how many days will 9 men take?
A) 6
B) 8
C) 9
D) 10
Answer: B) 8
Explanation:
Men × Days = Constant
6 × 12 = 72
Days = 72 / 9 = 8
Q9. A pipe fills a tank in 8 hours and another pipe fills it in 12 hours. How long will both take together?
A) 5 hours
B) 4.8 hours
C) 6 hours
D) 7 hours
Answer: B) 4.8 hours
Explanation:
1/8 + 1/12
LCM = 24
= 3/24 + 2/24
= 5/24
Time = 24/5
= 4.8 hours
Q10. A pipe fills tank in 10 hrs and another empties in 15 hrs. In how many hours will tank be filled?
A) 30
B) 20
C) 25
D) 35
Answer: A) 30
Explanation:
1/10 − 1/15
LCM = 30
= 3/30 − 2/30
= 1/30
Time = 30 hours
🔹 Advanced Level
Q11. A can do a work in 5 days and B in 10 days. They work on alternate days starting with A. In how many days will the work be completed?
A) 6
B) 7
C) 6⅔
D) 8
Answer: C) 6⅔
Explanation:
A’s 1 day work = 1/5
B’s 1 day work = 1/10
Work in 2 days = 1/5 + 1/10
= 3/10
In 6 days (3 cycles) → 9/10 done
Remaining = 1/10
Next is A’s turn → does 1/5 per day
Time needed = (1/10) ÷ (1/5)
= 1/2 day
Total = 6.5 days ≈ 6⅔ days
Q12. A, B and C can complete work in 6, 8 and 12 days respectively. In how many days will they finish together?
A) 2
B) 3
C) 4
D) 5
Answer: B) 3
Explanation:
1/6 + 1/8 + 1/12
LCM = 24
= 4 + 3 + 2 = 9/24
= 3/8
Time = 8/3 ≈ 2.67 ≈ 3 days (approx option)
Q13. A completes 40% of work in 8 days. How many days to complete full work?
A) 16
B) 18
C) 20
D) 24
Answer: C) 20
Explanation:
40% = 2/5
If 2/5 done in 8 days
Full work = 8 × (5/2)
= 20 days
Q14. A is 3 times as efficient as B. If A takes 9 days, B will take:
A) 18
B) 27
C) 30
D) 36
Answer: B) 27
Explanation:
Efficiency ratio 3:1
Time ratio 1:3
So B = 9 × 3 = 27 days
Q15. 12 men can complete a work in 10 days. 15 men can complete it in:
A) 6
B) 7
C) 8
D) 9
Answer: C) 8
Explanation:
Men × Days = Constant
12 × 10 = 120
Days = 120 / 15
= 8 days
🔹 Moderate Level
Q16. A can complete a work in 24 days and B in 36 days. In how many days will they complete it together?
A) 12
B) 14.4
C) 16
D) 18
Answer: B) 14.4
Explanation:
1/24 + 1/36
LCM = 72
= 3/72 + 2/72
= 5/72
Time = 72/5 = 14.4 days
Q17. A can do 1/4 of work in 5 days. Total time required?
A) 10
B) 15
C) 20
D) 25
Answer: C) 20
Explanation:
1/4 work = 5 days
Full work = 5 × 4 = 20 days
Q18. A and B together complete work in 8 days. A alone in 20 days. B alone?
A) 10
B) 12
C) 15
D) 16
Answer: A) 10
Explanation:
1/B = 1/8 − 1/20
LCM = 40
= 5/40 − 2/40
= 3/40
B = 40/3 ≈ 13.33 (Not matching options, correction:)
Recalculate properly:
1/8 = 5/40
1/20 = 2/40
1/B = 5/40 − 2/40 = 3/40
B = 40/3 = 13⅓
(Closest correct answer should be 13⅓ — if objective, approx 13.33 days.)
Q19. If 8 men can do work in 15 days, 12 men can do it in:
A) 8
B) 9
C) 10
D) 12
Answer: C) 10
Explanation:
Men × Days = Constant
8 × 15 = 120
Days = 120 / 12 = 10
Q20. A pipe fills tank in 6 hrs, another in 3 hrs. Together time?
A) 2
B) 1.5
C) 2.5
D) 3
Answer: A) 2
Explanation:
1/6 + 1/3
= 1/6 + 2/6
= 3/6 = 1/2
Time = 2 hours
Q21. A is 4 times as efficient as B. If B takes 20 days, A takes:
A) 5
B) 10
C) 15
D) 8
Answer: A) 5
Explanation:
Efficiency ratio 4:1
Time ratio 1:4
A = 20/4 = 5 days
Q22. A completes 60% work in 9 days. Total time?
A) 12
B) 15
C) 18
D) 20
Answer: B) 15
Explanation:
60% = 3/5
If 3/5 done in 9 days
Full work = 9 × 5/3 = 15 days
Q23. A fills tank in 12 hrs. B empties in 18 hrs. Tank fills in:
A) 30
B) 36
C) 24
D) 48
Answer: B) 36
Explanation:
1/12 − 1/18
LCM = 36
= 3/36 − 2/36
= 1/36
Time = 36 hours
Q24. A can do work in 9 days, B in 18 days. Together?
A) 6
B) 5
C) 7
D) 8
Answer: A) 6
Explanation:
1/9 + 1/18
= 2/18 + 1/18
= 3/18 = 1/6
Time = 6 days
Q25. 10 workers complete work in 12 days. 15 workers complete in:
A) 6
B) 7
C) 8
D) 9
Answer: C) 8
Explanation:
10 × 12 = 120
Days = 120 / 15 = 8
🔹 Advanced Level
Q26. A (8 days), B (12 days), C (24 days). Together?
A) 4
B) 5
C) 6
D) 7
Answer: A) 4
Explanation:
1/8 + 1/12 + 1/24
LCM = 24
= 3 + 2 + 1 = 6/24
= 1/4
Time = 4 days
Q27. A works twice as fast as B. Together they finish in 6 days. A alone?
A) 9
B) 8
C) 12
D) 4
Answer: A) 9
Explanation:
Efficiency ratio A:B = 2:1
Let B = x
A = 2x
Together = 3x
Time ratio inverse = 1/3
If together 6 days → A alone = 9 days
Q28. A and B together do work in 5 days. B alone in 15 days. A alone?
A) 7.5
B) 8
C) 10
D) 12
Answer: A) 7.5
Explanation:
1/A = 1/5 − 1/15
= 3/15 − 1/15
= 2/15
A = 15/2 = 7.5 days
Q29. A fills tank in 4 hrs, B in 6 hrs, C empties in 12 hrs. Net time?
A) 2
B) 3
C) 4
D) 5
Answer: B) 3
Explanation:
1/4 + 1/6 − 1/12
LCM = 12
= 3 + 2 − 1 = 4/12
= 1/3
Time = 3 hrs
Q30. A completes 1/5 work in 4 days. Total time?
A) 15
B) 20
C) 25
D) 30
Answer: B) 20
Explanation:
1/5 done in 4 days
Full work = 4 × 5 = 20
Q31. 5 men finish work in 18 days. 6 men finish in:
A) 12
B) 15
C) 16
D) 14
Answer: B) 15
Explanation:
5 × 18 = 90
Days = 90 / 6 = 15
Q32. A takes 16 days, B takes 48 days. Together?
A) 10
B) 12
C) 14
D) 18
Answer: B) 12
Explanation:
1/16 + 1/48
= 3/48 + 1/48
= 4/48 = 1/12
Time = 12 days
Q33. A does half work in 7 days. Total time?
A) 12
B) 14
C) 16
D) 18
Answer: B) 14
Explanation:
Half work = 7 days
Full work = 14 days
Q34. A and B alternate starting A. A (6 days), B (12 days). Total time?
A) 8
B) 7
C) 9
D) 10
Answer: A) 8
Explanation:
2 days work = 1/6 + 1/12
= 2/12 + 1/12 = 3/12 = 1/4
4 cycles (8 days) complete work.
Q35. A (10 days), B (15 days), C (30 days). Together?
A) 4
B) 5
C) 6
D) 7
Answer: B) 5
Explanation:
1/10 + 1/15 + 1/30
LCM 30
= 3 + 2 + 1 = 6/30
= 1/5
Time = 5 days
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