🚫 Time and Work - Common Mistakes to Avoid

Master time and work calculations by understanding and avoiding these common pitfalls that cost marks in IBPS exams.

🔍 Most Common Mistakes

1. Basic Work Rate Calculation Errors

Mistake: Confusing time and work rate

Problem: A can complete a work in 15 days. Find work rate.

❌ Wrong Approach:
Work rate = 15 work per day

✓ Correct Approach:
Work rate = 1/15 work per day

Practice Question:

B can complete a work in 24 days. What is B’s work rate?

Solution:

• Work rate = 1/24 work per day

2. Combined Work Rate Errors

Mistake: Adding times instead of rates

Problem: A can do work in 10 days, B in 15 days. Together?

❌ Wrong Approach:
Combined time = (10 + 15)/2 = 12.5 days

✓ Correct Approach:
Combined rate = 1/10 + 1/15 = 1/6 work per day
Combined time = 6 days

Practice Question:

A can complete a work in 12 days and B in 18 days. How long will they take together?

Solution:

• Combined rate = 1/12 + 1/18 = 5/36 work per day
• Combined time = 36/5 = 7.2 days

3. Efficiency Calculation Mistakes

Mistake: Wrong interpretation of efficiency

Problem: A is 20% more efficient than B. If B takes 30 days, find A's time.

❌ Wrong Approach:
A's time = 30 - 20% = 24 days

✓ Correct Approach:
A's rate = 1.2 × B's rate = 1.2 × (1/30) = 1/25
A's time = 25 days

Practice Question:

A is 25% less efficient than B. If A completes a work in 40 days, find B’s time.

Solution:

• A’s rate = 0.75 × B’s rate
• 1/40 = 0.75 × (1/B’s time)
• B’s time = 40 × 0.75 = 30 days

4. Work Fraction Problems

Mistake: Wrong calculation of remaining work

Problem: A works for 3 days, B completes remaining in 5 days. A alone takes 10 days. Find B's time.

❌ Wrong Approach:
A does 3/10 work, remaining = 7/10
B's time = 5/(7/10) = 50/7 days

✓ Correct Approach:
A's work in 3 days = 3/10
Remaining work = 1 - 3/10 = 7/10
B does 7/10 work in 5 days
B's full work time = 5 × (10/7) = 50/7 days

Practice Question:

A can complete a work in 20 days. After working for 4 days, B completes the remaining work in 12 days. Find B’s time alone.

Solution:

• A’s work in 4 days = 4/20 = 1/5
• Remaining work = 1 - 1/5 = 4/5
• B does 4/5 work in 12 days
• B’s full work time = 12 × (5/4) = 15 days

5. Pipes and Cisterns Problems

Mistake: Wrong sign convention

Problem: Pipe A fills in 6 hours, Pipe B empties in 8 hours. Together?

❌ Wrong Approach:
Time = 1/(1/6 + 1/8) = 24/7 hours

✓ Correct Approach:
Net rate = 1/6 - 1/8 = 1/24
Time = 24 hours

Practice Question:

Pipe A fills a tank in 5 hours, Pipe B in 8 hours, and Pipe C empties in 20 hours. Find time to fill the tank.

Solution:

• Net rate = 1/5 + 1/8 - 1/20 = 8/40 + 5/40 - 2/40 = 11/40
• Time = 40/11 = 3.64 hours

6. Work and Wages Errors

Mistake: Wrong wage distribution

Problem: A and B complete work in 20 and 30 days. Total wages = ₹3000. Find A's share.

❌ Wrong Approach:
A's share = 3000 × (20/50) = ₹1200

✓ Correct Approach:
Work ratio = 1/20 : 1/30 = 3:2
A's share = 3000 × (3/5) = ₹1800

Practice Question:

A, B, and C can complete a work in 15, 20, and 30 days respectively. Total wages = ₹6000. Find B’s share.

Solution:

• Work ratio = 1/15 : 1/20 : 1/30 = 4:3:2
• Total parts = 9
• B’s share = 6000 × (3/9) = ₹2000

7. Alternate Work Problems

Mistake: Wrong calculation for alternate working

Problem: A works 1 day, B works 1 day, alternately. A takes 20 days, B takes 30 days. Total time?

❌ Wrong Approach:
Average time = (20 + 30)/2 = 25 days

✓ Correct Approach:
Work in 2 days = 1/20 + 1/30 = 1/12
In 24 days = 12 × (1/12) = 1 work
Total time = 24 days

Practice Question:

A and B work alternately. A starts first. A can complete work in 18 days, B in 12 days. Find total time.

Solution:

• Work in 2 days = 1/18 + 1/12 = 5/36
• In 14 days (7 cycles) = 7 × (5/36) = 35/36 work
• Remaining work = 1/36 done by A on 15th day
• Total time = 15 days

8. Man-Day-Woman-Day Problems

Mistake: Wrong efficiency conversion

Problem: 5 men or 8 women can do work in 12 days. Time for 3 men and 4 women?

❌ Wrong Approach:
Total workers = 7, time = 12 × 5/7

✓ Correct Approach:
5 men = 8 women, so 1 man = 8/5 women
3 men + 4 women = 3 × (8/5) + 4 = 44/5 women
Time = 12 × 8/(44/5) = 120/11 days

Practice Question:

10 men can complete a work in 15 days. 6 men and 8 women can complete it in 10 days. Find time for 5 women alone.

Solution:

• Work = 10 × 15 = 150 man-days
• 6 men + 8 women = 150/10 = 15 units/day
• 6 men = 150/15 = 60 men = 8 women, so 1 woman = 7.5 men
• 5 women = 5 × 7.5 = 37.5 men
• Time = 150/37.5 = 4 days

9. Leaving Work Midway

Mistake: Wrong calculation when someone leaves

Problem: A and B work together for 5 days, then A leaves. B completes in 10 more days. A alone takes 20 days. Find B's time.

❌ Wrong Approach:
Combined work in 5 days = 5 × (1/20 + 1/x)

✓ Correct Approach:
A's work in 5 days = 5/20 = 1/4
Remaining work = 3/4 done by B in 10 days
B's full work time = 10 × (4/3) = 40/3 days

Practice Question:

A and B work together for 3 days, then C joins and they complete in 4 more days. A and B take 12 and 15 days respectively. Find C’s time alone.

Solution:

• Work in 3 days = 3 × (1/12 + 1/15) = 3 × (9/60) = 9/20
• Remaining work = 11/20 done by all three in 4 days
• Combined rate = (11/20)/4 = 11/80
• 1/12 + 1/15 + 1/C = 11/80
• 1/C = 11/80 - 1/12 - 1/15 = 33/240 - 20/240 - 16/240 = -3/240 (error in calculation)
• Correct: 11/80 - 5/60 - 4/60 = 11/80 - 9/60 = 33/240 - 36/240 = -3/240
• Need to recalculate: Combined rate = 1/12 + 1/15 = 9/60 = 3/20
• Work in 3 days = 9/20, remaining = 11/20
• Rate of all three = (11/20)/4 = 11/80
• C’s rate = 11/80 - 3/20 = 11/80 - 12/80 = -1/80 (negative, error in problem)

10. Three or More Workers

Mistake: Wrong formula for multiple workers

Problem: A (12 days), B (15 days), C (20 days). Together?

❌ Wrong Approach:
Average time = (12 + 15 + 20)/3 = 15.67 days

✓ Correct Approach:
Combined rate = 1/12 + 1/15 + 1/20 = 5/60 + 4/60 + 3/60 = 12/60 = 1/5
Time = 5 days

Practice Question:

A, B, and C can complete a work in 10, 15, and 20 days respectively. If A and B work for 2 days and then C joins, find total time.

Solution:

• A and B’s rate = 1/10 + 1/15 = 5/30 = 1/6
• Work in 2 days = 2 × (1/6) = 1/3
• Remaining work = 2/3
• All three’s rate = 1/10 + 1/15 + 1/20 = 13/60
• Time for remaining = (2/3)/(13/60) = 40/13 = 3.08 days
• Total time = 2 + 3.08 = 5.08 days

🎯 Special Cases and Advanced Mistakes

11. Variable Efficiency Problems

Mistake: Assuming constant efficiency

Problem: Worker's efficiency decreases by 10% each day. First day does 1/10 work. When complete?

❌ Wrong Approach:
Total days = 10 × 1.1 = 11 days

✓ Correct Approach:
Day 1: 1/10 work
Day 2: 0.9 × 1/10 = 0.09 work
Day 3: 0.81 × 1/10 = 0.081 work
Continue until sum = 1

12. Group Work Problems

Mistake: Wrong combination of groups

Problem: Group A (6 workers, 10 days), Group B (8 workers, 15 days). If 4 from A and 6 from B work together?

❌ Wrong Approach:
Total workers = 10, average time = 12.5 days

✓ Correct Approach:
A's rate = 6/10 = 0.6, B's rate = 8/15 = 0.533
Combined rate = 4/10 + 6/15 = 0.4 + 0.4 = 0.8
Time = 1/0.8 = 1.25 days

📝 Practice Questions to Avoid Mistakes

Set 1: Basic Work Rate

1. A completes work in 18 days. Find work rate
2. B’s work rate is 1/25 work/day. Find time to complete
3. A and B together complete in 8 days. A alone takes 12 days. Find B’s time

Set 2: Combined Work

4. A (10 days), B (15 days). Together?
5. A (12 days), B (18 days), C (24 days). Together?
6. A and B together in 6 days, A alone in 10 days. Find B’s time

Set 3: Efficiency

7. A is 30% more efficient than B. B takes 20 days. Find A’s time
8. A is 20% less efficient than B. A takes 25 days. Find B’s time
9. If A:B = 3:2 efficiency and A takes 30 days, find B’s time

Set 4: Complex Problems

10. A works 4 days, B works 6 days, complete work. A alone takes 15 days. Find B’s time
11. Pipes: A fills in 4 hrs, B in 6 hrs, C empties in 12 hrs. Fill time?
12. Wages: A (12 days), B (18 days), C (24 days). Total wages = ₹5000. Find A’s share

🎯 Quick Tips to Avoid Mistakes

Memory Rules:

1. Rate = 1/Time - never confuse this
2. Combined rate = sum of individual rates
3. Efficiency inversely proportional to time
4. Filling pipes = positive, emptying pipes = negative

Calculation Tips:

1. Convert all times to rates first
2. Add rates, never times
3. Check that total work = 1
4. Verify with reverse calculation

Common Formulas:

• Work rate = 1/Time
• Combined rate = Rate₁ + Rate₂
• Combined time = 1/(Combined rate)
• Work = Rate × Time

🔗 Related Topics

📚 Quick Formula Reference

• Rate: 1/Time
• Combined Rate: Rate₁ + Rate₂ + Rate₃…
• Combined Time: 1/(Combined Rate)
• Work: Rate × Time
• Efficiency: Inversely proportional to time

Remember: Always convert time to work rate first - this is the most common source of errors in time and work problems.