Time, Work and Pipes & Cisterns
Why This Chapter Matters
Time and Work gives 2-4 questions in SSC CGL and CHSL. Pipes and Cisterns is the same concept applied to filling/emptying tanks. Master the efficiency method — fastest approach.
Core Concepts
1. Work Efficiency Method (Best for SSC)
If A completes work in n days → A's 1-day work = 1/n → efficiency = 1/n
LCM method (fastest):
Take LCM of all given days as total work units.
Assign individual daily work = Total work / Days.
Work done together in 1 day = sum of efficiencies.
Days to complete = Total work / Combined efficiency.
Example: A takes 12 days, B takes 8 days. Together?
LCM(12,8)=24. A's efficiency=24/12=2 units/day. B's=24/8=3 units/day.
Combined=5 units/day. Days=24/5=4.8 days.
2. Standard Formulas
A takes a days, B takes b days, together: T = ab/(a+b)
A+B take T days, A alone takes a days, B alone: b = aT/(a-T)
3. Work Done in Parts
A alone for d days, then A+B together for remaining:
Work by A in d days = d/a. Remaining = 1-d/a. B+A together: (a+b) days for full → rate = 1/T.
4. Men, Days, Hours
M₁D₁H₁/W₁ = M₂D₂H₂/W₂
More men → fewer days (inverse). More work → more days (direct).
5. Pipes and Cisterns
Inlet pipe fills tank in a hours → fills 1/a per hour (positive).
Outlet pipe empties tank in b hours → empties 1/b per hour (negative).
Net work per hour = 1/a - 1/b.
Time to fill = ab/(b-a) [when b>a, otherwise overflows].
Both inlet and outlet open:
Net rate = sum of all inlets - sum of all outlets.
Solved Examples
Q1: A can do a work in 15 days, B in 20 days. A works for 6 days then B joins. How many more days for B to finish?
A in 6 days does: 6/15 = 2/5. Remaining: 3/5.
A+B together rate = 1/15+1/20 = 7/60.
Days = (3/5)/(7/60) = (3/5)×(60/7) = 36/7 ≈ 5.14 days.
Q2: Pipe A fills tank in 6 hrs, B in 4 hrs, C empties in 12 hrs. All open — how long to fill?
Net rate = 1/6+1/4-1/12 = 2/12+3/12-1/12 = 4/12 = 1/3.
Time = 3 hours.
Q3: 12 men complete work in 18 days. How many men to complete in 12 days?
M₁D₁=M₂D₂ → 12×18=M₂×12 → M₂=18 men.
PYQs (SSC)
SSC CGL 2023: A does work in 20 days, B in 30 days. They work alternate days starting with A. When is work done?
In 2 days: 1/20+1/30=1/12. For 12 pairs=24 days: 12×(1/12)=1. Work done in 24 days.
SSC CHSL 2022: Pipe A fills in 24 min, B fills in 32 min. Both open for 8 min, then B closed. Time for A alone to finish?
In 8 min: 8(1/24+1/32) = 8×7/96 = 7/12. Remaining: 5/12. A alone: (5/12)×24=10 min. Total=18 min.