Combined Work (Time & Work)
SSC GD Exam Preparation - Quantitative Aptitude
1️⃣ What is Combined Work?
When two or more people work together, their efficiencies (1-day work) are added.
Together = Add individual efficiencies
2️⃣ Key Formula
If:
A alone = x days → 1-day work = 1/x
B alone = y days → 1-day work = 1/y
Combined 1-day Work
1/x + 1/y
Combined Time
Time = 1 / (1/x + 1/y)
3️⃣ For 3 people (A, B, C)
Combined 1-day work = 1/x + 1/y + 1/z
4️⃣ Important Concepts
They work together = Add 1-day works
One leaves = Subtract his 1-day work
Work done = Time × 1-day work
If total work (LCM method) used → Easy to calculate individual shares
🧠 15 Practice Questions (With Answers)
Test your combined work concepts with these SSC GD level practice questions. Click on "View Answer" to check your understanding.
Q1. A can do a work in 12 days and B in 8 days. How long will both take together?
View Answer
1-day work = 1/12 + 1/8 = 5/24, Time = 24/5 = 4.8 days
Q2. A = 10 days, B = 20 days. Combined time?
View Answer
1-day work = 1/10 + 1/20 = 3/20, Time = 20/3 = 6.67 days
Q3. A = 6 days, B = 4 days. Combined time?
View Answer
1-day work = 1/6 + 1/4 = 5/12, Time = 12/5 = 2.4 days
Q4. A = 15 days, B = 30 days. Combined time?
View Answer
1-day work = 1/15 + 1/30 = 1/10, Time = 10 days
Q5. A = 12 days, B = 18 days, C = 36 days. Time together?
View Answer
1-day work = 1/12 + 1/18 + 1/36 = 1/6, Time = 6 days
Q6. A finishes work in 8 days, B in 16 days. After 3 days A leaves. Remaining time for B?
View Answer
1-day(A+B) = 1/8 + 1/16 = 3/16, Work in 3 days = 9/16, Remaining = 7/16, B alone = (7/16) ÷ (1/16) = 7 days
Q7. A = 20 days, B = 25 days. Work together for 5 days then B leaves. Remaining time for A?
View Answer
Combined 1-day = 1/20 + 1/25 = 9/100, Work in 5 days = 45/100 = 9/20, Remaining = 11/20, A's 1-day = 1/20, Time = (11/20)/(1/20) = 11 days
Q8. A does half work in 8 days. How long for full work with same speed?
View Answer
Half work → 8 days, Full work → 16 days
Q9. A completes work in 12 days, B is 50% as efficient. Combined time?
View Answer
B's time = 12 × 2 = 24, 1-day work = 1/12 + 1/24 = 1/8, Time = 8 days
Q10. A can do a work in 18 days, B in 6 days. A works 2 days, B finishes remaining. Total time?
View Answer
A's 2-day work = 2/18 = 1/9, Remaining = 8/9, B's 1-day work = 1/6, Time = (8/9) ÷ (1/6) = (8/9)×6 = 16/3 = 5.33 days total
Q11. A, B can together do a job in 12 days. A alone in 20 days. Find B's time.
View Answer
1-day(B) = 1/12 − 1/20 = 1/30, Time = 30 days
Q12. A = 5 days, B = 10 days, C = 20 days. How long together?
View Answer
1-day = 1/5 + 1/10 + 1/20 = 7/20, Time = 20/7 = 2.86 days
Q13. A & B together in 8 days. A alone = 12 days. B alone?
View Answer
1-day(B) = 1/8 − 1/12 = 1/24, B's time = 24 days
Q14. A = 9 days, B = 18 days. If they work 3 days together, how much work left?
View Answer
1-day = 1/9 + 1/18 = 1/6, 3-day work = 1/2, Remaining = 1/2
Q15. A can do a work in 30 days, B in 40 days. C helps A & B for 5 days, and they complete 1/4 work. Find C's 1-day work.
View Answer
A + B = 1/30 + 1/40 = 7/120, Let C's 1-day work = x, (7/120 + x) × 5 = 1/4, 7/24 + 5x = 1/4, 5x = 1/4 − 7/24 = (6 − 7)/24 = −1/24, x = −1/120, C is doing negative work = making mistakes
✅ SSC GD Exam Strategy
🟢 Remember 1-day work addition for combined work
🟢 Practice work left calculations when someone leaves
🟢 Master finding individual time from combined time
🟢 Learn to handle three-person combinations
🟢 Time yourself - aim for 45-60 seconds per combined work question
You've completed Combined Work Concepts!
SSC GD Tip: Combined work problems are very common in the quantitative section. Focus on mastering the concept of adding 1-day works when people work together. Remember to subtract when someone leaves, and practice scenarios with three people working together. The key is to convert all time values to 1-day work rates first, then perform the necessary calculations. Regular practice with previous year SSC GD questions will build your speed and accuracy in solving combined work problems efficiently.
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