Time and Work Shortcuts and Formulas (with Solved Questions)

Learn time and work shortcuts for placement aptitude tests: the LCM method, efficiency tricks, the men-days-hours formula, 15 solved questions and 10 practice questions with answers.

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Why Time and Work Is a Must-Prepare Topic

Time and work questions appear in the quantitative section of almost every placement aptitude test, including TCS NQT, Infosys, Wipro, Accenture, Cognizant and Capgemini. They also form the base for related topics such as pipes and cisterns and work-and-wages problems.

Most students solve these questions with fractions like 1/10 + 1/15, which is slow and easy to get wrong under time pressure. The faster way is the LCM (total work) method, which turns every question into simple whole-number arithmetic.

This guide covers the core idea, seven shortcuts, 15 solved placement-style questions and a 10-question practice set with answers. Time and work uses ratios heavily, so if you have not read it yet, start with our Ratio and Proportion guide.

The Core Idea: Work, Time and Efficiency

Every time and work question rests on one relationship:

Work = Efficiency (work per day) × Time

If A can finish a job in 10 days, A completes 1/10 of the job each day. That daily share is A's efficiency.

Two rules follow from this, and you will use them in almost every question:

  • Time and efficiency are inversely proportional. If A is twice as efficient as B, A takes half the time.
  • Work done adds up. When people work together, add their daily work, not their days.

A very common mistake is to add days: if A takes 10 days and B takes 15 days, together they do not take 25 days. Working together, they must finish faster than either of them alone.

7 Time and Work Shortcuts

Shortcut 1: The LCM (Total Work) Method

Assume the total work equals the LCM of everyone's days. Then each person's efficiency is a whole number of units per day.

Example: A takes 10 days, B takes 15 days. LCM = 30 units. A does 30 ÷ 10 = 3 units per day and B does 30 ÷ 15 = 2 units per day. Together they do 5 units per day, so they need 30 ÷ 5 = 6 days.

This method works for almost every question type, and it avoids fractions completely.

Shortcut 2: Two People Working Together

For two people, there is a direct formula:

Together time = (a × b) ÷ (a + b)

Example: A takes 10 days and B takes 15 days. (10 × 15) ÷ (10 + 15) = 150 ÷ 25 = 6 days.

Shortcut 3: Finding One Person's Time from the Team

If A and B together take x days and A alone takes y days, then B alone takes:

B alone = (x × y) ÷ (y − x)

Example: A and B together take 8 days, and A alone takes 12 days. B = (8 × 12) ÷ (12 − 8) = 96 ÷ 4 = 24 days.

Shortcut 4: Efficiency Ratio

If A is k times as efficient as B, then the time ratio is the reverse: A : B = 1 : k. When a question gives efficiency, give each person that many units per day.

Example: A is twice as efficient as B, and together they finish in 14 days. Let A = 2 units/day and B = 1 unit/day. Total work = 3 × 14 = 42 units. A alone takes 42 ÷ 2 = 21 days.

Shortcut 5: Pairs Working Together

When the question gives A+B, B+C and C+A, add all three. Each person is counted twice, so divide by 2 to get A+B+C.

(A + B + C) per day = [(A+B) + (B+C) + (C+A)] ÷ 2

Shortcut 6: The Men-Days-Hours Formula

When the number of workers, days or hours per day changes, use:

(M₁ × D₁ × H₁) ÷ W₁ = (M₂ × D₂ × H₂) ÷ W₂

M = men, D = days, H = hours per day, W = work. If the work is the same, ignore W.

Example: 10 men working 6 hours a day finish a job in 18 days. 15 men working 8 hours a day need (10 × 6 × 18) ÷ (15 × 8) = 1,080 ÷ 120 = 9 days.

Shortcut 7: Work and Wages

When people are paid for a job done together, wages are shared in the ratio of work done. If they work the same number of days, that is simply the ratio of their efficiencies.

Example: A can do a job in 6 days and B in 8 days. Using LCM 24, A = 4 units and B = 3 units per day, so wages are shared 4 : 3.

15 Solved Time and Work Questions

These questions follow the style used in campus aptitude tests. Try each one for about 45 seconds before reading the solution.

Q1. A can finish a job in 10 days and B in 15 days. How long will they take together?

LCM = 30. A = 3, B = 2 units/day. Together 5 units/day, so 30 ÷ 5. Answer: 6 days

Q2. A, B and C can do a job in 12, 18 and 36 days. How long will all three take together?

LCM = 36. A = 3, B = 2, C = 1 unit/day. Together 6 units/day, so 36 ÷ 6. Answer: 6 days

Q3. A and B together finish a job in 8 days. A alone takes 12 days. How long does B alone take?

(8 × 12) ÷ (12 − 8) = 96 ÷ 4. Answer: 24 days

Q4. A is twice as efficient as B. Together they finish a job in 14 days. How long does A alone take?

A = 2, B = 1 unit/day. Work = 3 × 14 = 42 units. A alone = 42 ÷ 2. Answer: 21 days

Q5. A can do a job in 20 days and B in 30 days. They work together for 6 days, then A leaves. How long does B take to finish the rest?

LCM = 60. A = 3, B = 2. In 6 days they do 6 × 5 = 30 units. Remaining 30 units at 2 units/day. Answer: 15 days

Q6. 12 men can complete a job in 18 days. How many days will 27 men take?

Men × days is constant: 12 × 18 = 216, so 216 ÷ 27. Answer: 8 days

Q7. 10 men working 6 hours a day complete a job in 18 days. How many days will 15 men working 8 hours a day take?

(10 × 6 × 18) ÷ (15 × 8) = 1,080 ÷ 120. Answer: 9 days

Q8. A can finish a job in 6 days and B in 8 days. Together they earn ₹2,800 for it. What is A's share?

LCM = 24. A = 4, B = 3 units/day, so wages are 4 : 3. A gets 4/7 × 2,800. Answer: ₹1,600

Q9. A and B can do a job in 12 days, B and C in 15 days, and C and A in 20 days. How long will A, B and C take together, and A alone?

LCM = 60. A+B = 5, B+C = 4, C+A = 3. Sum = 12, so A+B+C = 6 units/day, giving 60 ÷ 6 = 10 days. A = 6 − (B+C) = 6 − 4 = 2, so A alone = 60 ÷ 2 = 30 days. Answer: 10 days together; A alone 30 days

Q10. A can do a job in 15 days and B in 10 days. A works alone for 5 days, then B joins. How many days does the whole job take?

LCM = 30. A = 2, B = 3. A does 5 × 2 = 10 units alone. Remaining 20 units at 5 units/day = 4 days. Total = 5 + 4. Answer: 9 days

Q11. A can do a job in 16 days and B in 12 days. They work on alternate days, starting with A. How long does the job take?

LCM = 48. A = 3, B = 4. Every 2 days they do 7 units. After 12 days: 6 × 7 = 42 units. Day 13 (A): 45 units. The last 3 units take B 3/4 of a day. Total = 13 + 3/4. Answer: 13¾ days

Q12. A completes 1/3 of a job in 5 days and B completes 2/5 of it in 10 days. How long will they take together?

A alone takes 15 days and B alone takes 25 days. (15 × 25) ÷ (15 + 25) = 375 ÷ 40. Answer: 9⅜ days

Q13. A is 50% more efficient than B. B alone takes 30 days. How long will they take together?

A takes 30 ÷ 1.5 = 20 days. Together = (20 × 30) ÷ (20 + 30) = 600 ÷ 50. Answer: 12 days

Q14. 20 women can finish a job in 16 days, and 16 men can finish it in 15 days. What is the ratio of a man's efficiency to a woman's?

Total work: 20 × 16 = 320 woman-days and 16 × 15 = 240 man-days. So 240 men-days = 320 women-days, and 1 man = 4/3 women. Answer: 4 : 3

Q15. A can do a job in 18 days and B in 24 days. With C's help, they finish it in 8 days. How long would C take alone?

LCM = 72. A = 4, B = 3. All three do 72 ÷ 8 = 9 units/day, so C = 9 − 4 − 3 = 2 units/day. C alone = 72 ÷ 2. Answer: 36 days

10 Practice Questions (Answers Below)

Set a timer for 10 minutes and solve all ten without a calculator.

  1. A can do a job in 6 days and B in 12 days. How long will they take together?
  2. A, B and C can do a job in 10, 15 and 30 days. How long will all three take together?
  3. A and B together take 10 days. A alone takes 15 days. How long does B alone take?
  4. 24 men can finish a job in 15 days. How many days will 20 men take?
  5. A is twice as efficient as B. Together they finish in 12 days. How long does A alone take?
  6. 8 men working 9 hours a day finish a job in 20 days. How many days will 12 men working 8 hours a day take?
  7. A can do a job in 20 days and B in 25 days. Together they earn ₹4,500. What is A's share?
  8. A can do a job in 12 days and B in 20 days. They work together for 3 days, then A leaves. How long does B take to finish?
  9. A and B can do a job in 12 days, B and C in 20 days, and C and A in 15 days. How long will all three take together?
  10. A finishes 2/3 of a job in 8 days. How long will A take for the whole job?

Answers

QAnswerQuick Method
14 days(6 × 12) ÷ 18
25 daysLCM 30: 3 + 2 + 1 = 6 units/day
330 days(10 × 15) ÷ (15 − 10)
418 days24 × 15 ÷ 20
518 daysWork = 3 × 12 = 36; A = 2/day
615 days(8 × 9 × 20) ÷ (12 × 8)
7₹2,500LCM 100: 5 : 4, so 5/9 × 4,500
812 daysLCM 60: 3 × 8 = 24 done; 36 ÷ 3
910 daysLCM 60: (5 + 3 + 4) ÷ 2 = 6/day
1012 days8 ÷ (2/3)

Scored 8 or more? You are ready for mixed sets. Scored less? Re-practise Shortcuts 1, 5 and 6, which cover most question types.

Common Mistakes and How to Avoid Them

Most wrong answers in time and work come from five habits:

  • Adding days instead of work. 10 days + 15 days is never the answer for working together. Add daily work.
  • Using fractions when LCM is faster. 1/12 + 1/18 + 1/36 invites errors. With LCM 36, it is just 3 + 2 + 1.
  • Reversing the efficiency ratio. If A is twice as efficient, A takes half the time, not double.
  • Ignoring hours per day. If the question mentions hours per day, include H in the men-days-hours formula.
  • Sharing wages by days instead of work. Wages follow the work done, which usually means the efficiency ratio.

How to Practise This Topic in One Week

  1. Days 1–2: Practise the LCM method on 20 basic "together" questions until it is automatic.
  2. Days 3–4: Solve "someone leaves or joins", alternate-day and pair (A+B, B+C, C+A) questions.
  3. Day 5: Practise men-days-hours and work-and-wages questions.
  4. Day 6: Take timed sets of 10 questions in 10 minutes.
  5. Day 7: Mix time and work with percentage, ratio and time, speed and distance questions.

In the real test, write the LCM and each person's units in the first line. It makes almost every question a two-step calculation. Section patterns change between hiring seasons, so check the latest pattern for your target company. Our TCS Aptitude Test Pattern guide is a useful reference.

Frequently Asked Questions

What is the basic formula for time and work?

Work = Efficiency × Time. If a person finishes a job in n days, they complete 1/n of the job each day.

What is the LCM method in time and work?

Take the total work as the LCM of everyone's days. Each person's daily work then becomes a whole number of units, which makes calculation quick and avoids fractions.

If A takes a days and B takes b days, how long do they take together?

Together they take (a × b) ÷ (a + b) days. For 10 and 15 days, that is 6 days.

How are wages shared in time and work questions?

Wages are shared in the ratio of work done. When people work the same number of days, this equals the ratio of their efficiencies.

Is pipes and cisterns the same as time and work?

It uses the same idea. A filling pipe works like a worker, and a leak or emptying pipe does negative work.

Final Word

Time and work becomes simple once you stop adding fractions and start using the LCM method. Learn the seven shortcuts, practise the 15 solved questions, and solve one timed set each day for a week.

Continue your aptitude preparation with Percentage Shortcuts, Ratio and Proportion, Profit and Loss Shortcuts and our complete Aptitude Test Preparation Tips guide.

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