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SSC MTS Basic Time & Work

Study Material — 2 PYQs (2021–2021) · Concept Notes · Shortcuts

SSC MTS Basic Time & Work is a frequently tested subtopic — 2 previous year questions from 2021–2021 papers are included below with concept notes, key rules and shortcut tricks.

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2021–2021
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Previous Year Questions

SSC MTS Basic Time & Work — Past Exam Questions

2 questions from actual SSC MTS papers · all shown free · click option to reveal solution

Exam Q 12021Previous Year Pattern

If 5 workers can build a wall in 20 days, how many days will 10 workers take to build the same wall?

Exam Q 22021Previous Year Pattern

Two workers, M and N, working together can complete a job in 6 days. If M works alone, he takes 9 days more than N. How many days does N take to complete the job alone?

Concept Notes

Basic Time & Work— Rules & Concept

Core ConceptRead this first — the foundation of the topic
Core Concept

Work is always considered as 1 unit (complete job). If A can complete work in 10 days, A's rate of work is 1/10 per day. This means A completes 1/10th of the total work each day

Key Rules

Work = Rate × Time. If multiple people work together, their rates add up. Total work is always 1 unit. Rate of work = 1/Time taken to complete the job

Basic Formulas

- If A completes work in 'a' days, A's one day work = 1/a - If A and B together complete work in 'd' days, (1/a + 1/b) = 1/d - Time taken by A and B together = (a × b)/(a + b) days - If A completes work in 'x' days and B in 'y' days, working together they complete in xy/(x+y) days

Exam PatternsWhat examiners ask — read before attempting PYQs

SSC CGL typically asks 2-3 questions from this topic. Common patterns include: two people working together, one person leaving midway, comparing efficiencies, and alternative work scenarios.

ShortcutsUse these to save 30–60 seconds per question

- LCM Method: Take LCM of all time periods given. This becomes total work. Then find individual rates by dividing LCM by individual time.

This eliminates fractions and makes calculations faster.

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

A's one day work = 1/12

2
Step 2

B's one day work = 1/18

3
Step 3

Combined one day work = 1/12 + 1/18 = (3+2)/36 = 5/36

4
Step 4

Time taken together = 36/5 = 7.2 days Alternative (Shortcut): Time = (12 × 18)/(12 + 18) = 216/30 = 7.2 days Worked Example 2: A and B together can complete work in 6 days. A alone can complete it in 10 days. In how many days can B alone complete the work?

1
Step 1

Combined one day work = 1/6

2
Step 2

A's one day work = 1/10

3
Step 3

B's one day work = 1/6 - 1/10 = (5-3)/30 = 2/30 = 1/15

4
Step 4

B alone can complete work in 15 days Shortcut Formula: If A and B together complete work in T days and A alone in A days, then B alone takes: B = (A × T)/(A - T) days Applying: B = (10 × 6)/(10 - 6) = 60/4 = 15 days Most Common Trap: Students often add time instead of adding rates. Remember - when people work together, their RATES add up, not their TIME. If A takes 4 days and B takes 6 days, together they DON'T take 4+6=10 days. Instead, calculate 1/4 + 1/6 to find combined rate. Another Major Mistake: Forgetting that work is always 1 unit. Students sometimes assume work quantity changes, leading to wrong calculations. Always treat complete work as 1 unit regardless of the scenario. Efficiency Trick: If A is twice as efficient as B, then A takes half the time B takes. If A:B efficiency ratio is 2:3, then their time ratio is 3:2 (inverse relationship). Negative Work Concept: Sometimes one person does work while another undoes it (like filling and emptying a tank). In such cases, subtract the rates instead of adding them.

Key Points to Remember

  • Work is always considered as 1 complete unit in all problems
  • Rate of work = 1/Time taken to complete the job alone
  • When working together, rates add up: 1/a + 1/b = 1/combined time
  • Combined time formula: (a × b)/(a + b) where a, b are individual times
  • LCM method eliminates fractions - take LCM of all given times as total work
  • Efficiency and time have inverse relationship - higher efficiency means less time
  • If A is n times efficient than B, then A takes 1/n times the time B takes
  • In problems with destructive work, subtract rates instead of adding
  • Never add individual times to get combined time - this is the biggest trap
  • Work = Rate × Time is the fundamental equation for all variations

Exam-Specific Tips

  • Combined work formula: Time = (a × b)/(a + b) days
  • If A and B work together for T days and A alone for remaining, use: 1 = T(1/a + 1/b) + remaining_time(1/a)
  • Efficiency ratio of 2:3 means time ratio of 3:2
  • If A completes work in 'a' days, A's rate = 1/a work per day
  • LCM method: Total work = LCM of all individual times
  • For pipes: Inlet rate positive, outlet rate negative
  • Work done = Rate × Time, where total work = 1 unit
  • If A can do work in x days and B in y days, together they need xy/(x+y) days

60-Second Revision — Basic Time & Work

  • Formula: Combined time = (a × b)/(a + b) for two people working together
  • Remember: Add RATES, never add TIME when people work together
  • Trap: Don't assume 4 days + 6 days = 10 days together
  • Quick method: Use LCM of times as total work to avoid fractions
  • Efficiency rule: Higher efficiency = Less time (inverse relation)
  • Standard approach: Find individual rates, add them, then find combined time
  • Check: Combined time should always be less than individual times
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