Solved Examples
Time and Work · Study material
Solved Examples – Work & Time
Solved examples help students understand the practical application of Work & Time concepts in competitive examinations. These examples are designed from basic to advanced level and cover important Work & Time problems frequently asked in SSC, Banking, Railway, CDS, NDA, CAT, UPSC, and placement aptitude tests.
Topics Covered in Solved Examples
- One Day Work Problems
- Combined Work Problems
- Efficiency-Based Questions
- Men-Days-Hours Problems
- Pipes and Cisterns Applications
- Alternate Working Problems
- Partial Work Problems
- Work Distribution Problems
- Wages and Productivity
- Advanced Work & Time Applications
Example 1: One Day Work Problem
Question: A can complete a work in 12 days. Find A's one day's work.
Solution:
One day's work:
= 1/12
Therefore:
A's one day's work = 1/12
Example 2: Combined Work Problem
Question: A can complete a work in 10 days and B can complete the same work in 15 days. In how many days will they complete the work together?
Solution:
A's one day's work:
= 1/10
B's one day's work:
= 1/15
Combined work:
= 1/10 + 1/15
= 5/30
= 1/6
Therefore:
They complete the work in 6 days.
Example 3: Using Shortcut Formula
Question: A completes a work in 12 days and B in 18 days. Find the time taken together.
Solution:
Using formula:
= xy / (x + y)
= (12 × 18) / (12 + 18)
= 216/30
= 7.2 days
Therefore:
Required time = 7.2 days
Example 4: Efficiency Problem
Question: A is twice as efficient as B. If B completes a work in 24 days, in how many days will A complete it?
Solution:
A is 2 times more efficient.
Time is inversely proportional to efficiency.
A's time:
= 24/2
= 12 days
Therefore:
A completes the work in 12 days.
Example 5: Men and Days Problem
Question: 12 men can complete a work in 15 days. How many men are needed to complete the same work in 9 days?
Solution:
Men and days are inversely proportional.
12 × 15 = x × 9
180 = 9x
x = 20
Therefore:
Required men = 20
Example 6: Men-Days-Hours Problem
Question: 10 men working 8 hours daily complete a work in 12 days. In how many days will 15 men working 6 hours daily complete the same work?
Solution:
Using:
Men × Days × Hours = Constant
10 × 12 × 8 = 15 × x × 6
960 = 90x
x = 10.67
Therefore:
Required days ≈ 10.67
Example 7: Pipes and Cisterns Problem
Question: A pipe fills a tank in 12 hours and another pipe fills it in 18 hours. In how many hours will both pipes fill the tank together?
Solution:
Combined work:
= 1/12 + 1/18
= 5/36
Therefore:
Time taken:
= 36/5
= 7.2 hours
Therefore:
Required time = 7.2 hours
Example 8: Filling and Emptying Pipe Problem
Question: A pipe fills a tank in 10 hours and another empties it in 15 hours. In how many hours will the tank be filled?
Solution:
Filling pipe work:
= 1/10
Emptying pipe work:
= -1/15
Net work:
= 1/10 − 1/15
= 1/30
Therefore:
Tank will fill in 30 hours.
Example 9: Three Persons Working Together
Question: A, B, and C complete a work in 12, 18, and 36 days respectively. Find the time taken together.
Solution:
Combined work:
= 1/12 + 1/18 + 1/36
= 3/18
= 1/6
Therefore:
They complete the work in 6 days.
Example 10: Partial Work Problem
Question: A completes half of a work in 6 days. In how many days will A complete the entire work?
Solution:
Half work takes:
= 6 days
Full work:
= 12 days
Therefore:
A completes the entire work in 12 days.
Example 11: Alternate Day Working Problem
Question: A completes a work in 12 days and B in 18 days. If they work on alternate days starting with A, in how many days will the work be completed?
Solution:
Work done in 2 days:
= 1/12 + 1/18
= 5/36
Work done in 12 days:
= 6 × 5/36
= 5/6
Remaining work:
= 1/6
A completes remaining work in:
= 2 days
Therefore:
Total time = 14 days
Example 12: Work Ratio Problem
Question: A and B together earn 900 for completing a work. If their efficiency ratio is 2 : 3, find their individual wages.
Solution:
Total ratio:
= 2 + 3
= 5
A's share:
= (2/5) × 900
= 360
B's share:
= (3/5) × 900
= 540
Therefore:
A receives 360 and B receives 540.
Example 13: Work and Efficiency Problem
Question: A is 50% more efficient than B. If B takes 30 days to complete a work, find the time taken by A.
Solution:
A's efficiency:
= 150%
Efficiency ratio:
= 3 : 2
Time ratio:
= 2 : 3
A's time:
= (2/3) × 30
= 20 days
Therefore:
A completes the work in 20 days.
Example 14: Advanced Combined Work Problem
Question: A can complete a work in 20 days and B in 30 days. They work together for 6 days. How much work remains?
Solution:
Combined work:
= 1/20 + 1/30
= 1/12
Work completed in 6 days:
= 6 × 1/12
= 1/2
Remaining work:
= 1 − 1/2
= 1/2
Therefore:
Remaining work = 1/2
Example 15: Worker Leaving Problem
Question: A completes a work in 15 days and B in 20 days. They start together, but B leaves after 4 days. In how many more days will A finish the remaining work?
Solution:
Combined work:
= 1/15 + 1/20
= 7/60
Work done in 4 days:
= 28/60
= 7/15
Remaining work:
= 1 − 7/15
= 8/15
A's one day's work:
= 1/15
Time required:
= (8/15) ÷ (1/15)
= 8 days
Therefore:
A finishes remaining work in 8 days.
Example 16: LCM Method Problem
Question: A completes work in 8 days and B in 12 days. Find the time taken together using LCM method.
Solution:
LCM of 8 and 12:
= 24
A's efficiency:
= 24/8
= 3
B's efficiency:
= 24/12
= 2
Combined efficiency:
= 5
Required time:
= 24/5
= 4.8 days
Therefore:
Required time = 4.8 days
Example 17: Work and Wage Distribution
Question: A can do a work in 10 days and B in 15 days. If total wage is 1500, find B's share.
Solution:
Efficiency ratio:
= 15 : 10
= 3 : 2
B's share:
= (2/5) × 1500
= 600
Therefore:
B's share = 600
Example 18: Advanced Work & Time Problem
Question: 24 men working 8 hours daily complete a work in 20 days. How many men working 10 hours daily are required to complete the same work in 16 days?
Solution:
Using:
Men × Days × Hours = Constant
24 × 20 × 8 = x × 16 × 10
3840 = 160x
x = 24
Therefore:
Required men = 24
Important Exam Tips
- Always calculate one day's work first.
- Use LCM method for faster calculations.
- Memorize combined work formulas.
- Practice alternate work problems regularly.
- Remember efficiency-time inverse relation.
- Use MDH formula carefully.
- Verify final calculations properly.
Practicing solved examples regularly improves conceptual clarity, logical thinking, and calculation speed in solving Work & Time questions in competitive examinations.