Time & Work
SSC-CGL Exams
1. Concept Overview
Every work-related question is based on a simple core idea:
Work = Rate × Time
If a person can complete a job in N days, then 1 day's work = 1/N part of the job.
Example 1
If A can complete a work in 10 days, then A's 1 day work = 1/10, so A can complete 1/10th of the work each day.
A's efficiency = 1/10 of work/day
2. Basic Formulas
| Concept | Formula | Example |
|---|---|---|
| Work & Time | Work = Rate × Time | - |
| One day's work | = 1/Time taken | - |
| Total Work | LCM of time taken by persons | To simplify calculation |
| Efficiency | Inversely proportional to Time | E ∝ 1/T |
| Combined Work | 1/T = 1/T₁ + 1/T₂ + ... | - |
Example 2
A can finish a work in 6 days, B in 12 days. Find how long they'll take together.
1/T = 1/6 + 1/12 = 1/4
They finish in 4 days
3. Work Efficiency Method
Instead of fractions, use LCM method for quick SSC solving.
Example 3
A can do a job in 8 days, B in 12 days.
→ LCM = 24 (assume total work = 24 units)
A's 1-day work = 24/8 = 3 units
B's 1-day work = 24/12 = 2 units
Together = 3 + 2 = 5 units/day
Time = 24/5 = 4.8 days
4.8 days
4. Pipes & Cisterns
These are work problems in flow form.
Inlet pipe
Fills the tank → positive work
Outlet pipe
Empties the tank → negative work
| Case | Formula |
|---|---|
| 1 pipe fills in T hrs | 1 hr work = 1/T |
| 1 pipe empties in T hrs | 1 hr work = −1/T |
| Both open | Net work/hr = (1/T₁ ± 1/T₂) |
Example 4
Pipe A fills a tank in 6 hrs, B fills in 4 hrs. Find time taken together.
1/T = 1/6 + 1/4 = 5/12
Tank filled in 12/5 = 2.4 hrs
Example 5
Pipe A fills a tank in 6 hrs, Pipe B empties it in 12 hrs. Both open together.
1/T = 1/6 - 1/12 = 1/12
Tank filled in 12 hrs
5. Wages & Combined Work
Wages are directly proportional to work done.
A's share = (A's work / Total work) × P
Example 6
A can do a job in 10 days, B in 15 days. They earn ₹600 together. Find A's share.
Total work = LCM(10,15)=30
A's 1-day = 3, B's 1-day = 2 → Together = 5
A's share = 3/5 × 600 = ₹360
A's share = ₹360
6. Combined & Alternate Work
Example 7
A and B together can complete work in 8 days. A alone can do it in 12 days. Find B's time alone.
1/B = 1/8 - 1/12 = 1/24
B alone takes 24 days
Example 8
A and B work alternately. A alone finishes in 10 days, B in 15 days. Find days required if they start alternately.
Total work = LCM(10,15)=30
A = 3 units/day, B = 2 units/day
In 2 days → 5 units done
30 ÷ 5 = 6 such cycles → 12 days total
12 days
7. Shortcut Formulas for SSC
| Case | Shortcut |
|---|---|
| Work done ∝ Efficiency | E ∝ 1/T |
| Combined work | 1/T = 1/T₁ + 1/T₂ |
| Pipes opposite | 1/T = 1/T₁ - 1/T₂ |
| Equal efficiency ratio | T₁/T₂ = E₂/E₁ |
| Work & Wages | Share = Work Ratio |
8. Example Set
Example 9
A can do a work in 15 days, B in 20 days, C in 30 days. In how many days will all finish together?
1/T = 1/15 + 1/20 + 1/30 = 1/6
6 days
Example 10
A can complete a work in 12 days, B in 18 days. A works for 4 days, then leaves. B completes the rest. Find total days.
Total work = LCM(12,18)=36
A=3 units/day, B=2 units/day
A's 4 days = 12 units
Remaining = 24 units → B takes 24/2=12 days
Total = 16 days
Example 11
Pipe A fills tank in 8 hrs, Pipe B empties in 12 hrs. Find net fill time.
1/T = 1/8 - 1/12 = 1/24
24 hours
9. Practice Section
Q1. A can do a job in 10 days, B in 20 days. How long if both work together?
View Answer
1/T = 1/10 + 1/20 = 3/20 ⇒ T = 6.67 days
6⅔ days
Q2. A and B can do a work in 12 and 16 days respectively. Find time if A leaves after 4 days.
View Answer
LCM=48, A=4u/day, B=3u/day
A 4 days = 16u, Remaining = 32u → B=32/3=10⅔ days
≈14⅔ days total
Q3. A can do a job in 15 days, B in 25 days. A works 3 days, B works 2 days alternately. In how many days work is completed?
View Answer
LCM=75, A=5u/day, B=3u/day
In 5 days = 21u, total 75u → (75/21)*5 ≈ 17.85 days
≈17.9 days
Q4. Two pipes fill tank in 12 and 15 hrs. A third pipe empties in 20 hrs. All open together.
View Answer
1/T = 1/12 + 1/15 - 1/20 = (5+4-3)/60 = 6/60 ⇒ T=10 hrs
10 hours
Q5. A, B, and C can complete a work in 10, 12, and 15 days respectively. If A leaves after 2 days, find remaining time.
View Answer
LCM=60, A=6, B=5, C=4 → All=15/day
A's 2 days = 12, remaining = 48 → B+C=9/day → 48/9=5⅓ days
≈7⅓ days total
Q6. A and B's efficiencies are in ratio 5:3. Together they finish in 8 days. Find A's alone time.
View Answer
Work ratio = 5:3 → Total=8 parts
If total work=8×8=64 → A's rate=5 → 64/5=12.8 days
12.8 days
Q7. A pipe fills tank in 4 hrs, another in 6 hrs, but outlet empties in 8 hrs. Find fill time.
View Answer
1/T=1/4+1/6−1/8= (6+4−3)/24=7/24 ⇒ T=24/7≈3.43 hrs
≈3 hrs 26 min
10. Quick Recap Table
| Topic | Formula / Concept | Shortcut |
|---|---|---|
| One day's work | 1/N | Inverse of time |
| Efficiency | ∝ 1/Time | Faster = more efficient |
| Combined work | 1/T = 1/T₁ + 1/T₂ | Add reciprocals |
| Pipes opposite | 1/T = 1/T₁ - 1/T₂ | Subtract reciprocals |
| Wages | Work ratio | Share = (work ratio × total) |
| Alternate work | Find per-cycle work | Divide total by per-cycle |
You've completed Article 8: Time & Work!
Courage Tip: For SSC CGL, questions are often framed to check your speed with LCM and unit-work logic — always start with "1 day's work" and end with "total work done = time × efficiency."
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