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SSC CGL Basic Time & Work

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This page covers SSC CGL Basic Time & Work with complete concept notes, 8 graded practice MCQs, key points and exam-specific tips. Free to study.

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Concept Notes

Basic Time & Work— Rules & Concept

Core ConceptRead this first — the foundation of the topic

BASIC TIME & WORK — COMPLETE GUIDE FOR SSC CGL ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

CORE CONCEPT ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Time and Work problems are about one simple idea: how fast can someone finish a job? If a person finishes a job in N days, then in ONE day they complete 1/N of the total work. This fraction is called their 'one day's work' or 'work rate'. Everything in this topic builds on this one idea.

Think of it like filling a tank. If you fill 1/5 of the tank each day, you fill the full tank in 5 days. Simple. ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

KEY RULES ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Rule 1: More workers = Less time (Inverse relationship) Rule 2: More work = More time (Direct relationship)

Rule 3: Total Work = Efficiency x Time Rule 4: When two people work together, ADD their one-day work fractions.

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Formula BlockMemorise — at least one formula appears in every paper

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• One day work of A = 1/a (if A finishes in 'a' days)
• Together (A+B) finish in = (a x b) / (a + b) days
• Together (A+B+C) one day work = 1/a + 1/b + 1/c

• If A is twice as fast as B, and B takes N days, then A takes N/2 days

• Work Done = Rate x Time
• Remaining Work = 1 - Work already done

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Exam PatternsWhat examiners ask — read before attempting PYQs

— WHAT GETS ASKED ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ SSC CGL regularly asks: 1. Two people working together — find total time 2. One person leaves early — find total time 3. Find how many days one person takes alone 4.

Efficiency ratio problems (A is twice as fast as B) 5. Fraction of work done in given days ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

ShortcutsUse these to save 30–60 seconds per question
1

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ TRICK 1 — LCM METHOD (Fastest for SSC) Instead of fractions, assign total work = LCM of all days given. Then calculate each person's efficiency (work per day) as a whole number. This kills fractions and saves 40 seconds per question. Example setup: A takes 6 days, B takes 12 days. LCM of 6 and 12 =

2

Total Work = 12 units. A's efficiency = 12/6 = 2 units/day B's efficiency = 12/12 = 1 unit/day Together = 3 units/day → Time = 12/3 = 4 days. Done. TRICK 2 — TWO-PERSON FORMULA If A takes 'a' days and B takes 'b' days, together they take: Time = (a x b) / (a + b) Memorize this. It is the most used formula in this topic. TRICK 3 — EFFICIENCY RATIO SHORTCUT If A is K times more efficient than B: Ratio of time taken = 1 : K (A takes less time) If A is 3 times as efficient as B and B takes 18 days → A takes 6 days. ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Worked ExampleSolve this step-by-step before moving on
1
Step 1

Use LCM method. LCM of 15 and 10 = 30.

2
Step 2

Total work = 30 units.

3
Step 3

A's efficiency = 30/15 = 2 units/day

4
Step 4

B's efficiency = 30/10 = 3 units/day

5
Step 5

Together = 2 + 3 = 5 units/day

6
Step 6

Time = 30/5 = 6 days Answer: 6 days Verify with formula: (15 x 10)/(15 + 10) = 150/25 = 6 days. Matches! ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ WORKED EXAMPLE 2 — One Person Leaves Early ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ Question: A can finish a job in 12 days. B can finish it in 16 days. They work together for 4 days. Then A leaves. How many more days does B need to finish the remaining work?

1
Step 1

LCM of 12 and 16 = 48. Total work = 48 units.

2
Step 2

A's efficiency = 48/12 = 4 units/day

3
Step 3

B's efficiency = 48/16 = 3 units/day

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Step 4

Work done together in 4 days = (4 + 3) x 4 = 28 units

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Step 5

Remaining work = 48 - 28 = 20 units

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Step 6

B alone does 3 units/day → Time = 20/3 = 6.67 days ≈ 6 and 2/3 days Answer: 6 and 2/3 days ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ NUMBER 1 COMMON TRAP — DON'T FALL FOR IT ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ TRAP: Students add days directly instead of adding work rates. WRONG thinking: A takes 6 days + B takes 12 days → Together = 18 days. NEVER do this! CORRECT thinking: ADD the work rates (1/6 + 1/12), NOT the days. This single mistake is responsible for the most wrong answers in Time & Work across all SSC exams. Always work with efficiencies or fractions — never add days.

Key Points to Remember

  • If a person completes work in N days, their one-day work = 1/N (this is their work rate).
  • Formula: Two people A and B together finish work in = (a × b) / (a + b) days.
  • LCM Method: Set Total Work = LCM of all given days to avoid fractions completely.
  • Efficiency = Total Work / Number of Days — always a whole number in LCM method.
  • When working together, ADD efficiencies (units/day), never add the number of days.
  • If A is K times more efficient than B, then A takes K times LESS time than B.
  • Remaining Work = 1 − (fraction of work already completed).
  • Total Work = Efficiency × Time — this triangle relationship solves every variation.
  • Shortcut: If A, B, C together do 1/x work per day, they finish the job in x days.
  • Trap: NEVER add days directly — always convert to rates/efficiencies before adding.

Exam-Specific Tips

  • Formula for two persons working together: Time = (a × b) / (a + b) — this is the single most tested formula in SSC CGL Time & Work.
  • If A does a work in 'a' days, A's one day work fraction = 1/a. This is the foundation of all Time & Work calculations.
  • LCM method assigns Total Work = LCM of all individual completion days, making all efficiencies whole numbers.
  • If A is twice as efficient as B, A takes exactly half the time B takes to complete the same work.
  • When A and B together complete work in T days and A alone takes 'a' days, B alone takes T×a / (a−T) days.
  • Work and Time are directly proportional — double the work, double the time (with same workers).
  • Workers and Time are inversely proportional — double the workers, half the time (for same work).
  • If A completes 1/3 of work in D days, A will complete full work in 3D days — scale linearly.
Practice MCQs

Basic Time & Work — Practice Questions

8graded MCQs · easy to hard · full solution & trap analysis

All MCQs →
Practice 1easy

B can finish a job in 15 days. In how many days can B finish 3/5 of the job?

Practice 2easy

If 8 workers can build a wall in 15 days, how many days will 12 workers take to build the same wall, assuming all workers work at the same rate?

Practice 3easy

E completes 1/4 of a work in 5 days. At this rate, how many days will E take to complete the entire work?

Practice 4easy

A can complete a piece of work in 12 days. How much work will A complete in 5 days?

Practice 5easy

B can finish a task in 18 days. How many days will B take to complete 2/3 of the task?

Practice 6easy

E can do 1/4 of a work in 6 days. In how many days can E complete the entire work?

Practice 7easy

F and G together complete a work in 10 days. F alone can complete it in 15 days. How much work does G do in 1 day?

Practice 8easy

C and D together can complete a work in 8 days. If C alone can do it in 12 days, in how many days can D alone complete the work?

60-Second Revision — Basic Time & Work

  • Formula: Two people together = (a × b) / (a + b) days — memorize and apply directly.
  • Trick: Always use LCM Method — set Total Work = LCM of days, find efficiencies as whole numbers, then divide.
  • Remember: ADD work rates (efficiencies), NEVER add the number of days — this is the #1 exam trap.
  • Remaining Work rule: After some days, Remaining Work = Total Work − Work Already Done, then divide by new rate.
  • Efficiency ratio: A is K times faster than B → A takes (1/K) times the days B takes.
  • Trap check: If your combined time is MORE than either individual time, your answer is WRONG — together is always faster.
  • Last-minute formula recap: One day work = 1/N | Together rate = 1/a + 1/b | Together time = ab/(a+b).
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