# Time and Work Questions with Answers, Formulas and Shortcuts

> Time and work formulas, pipes and cisterns, efficiency ratios and solved questions with step-by-step answers for placement aptitude preparation.

Source: https://www.sansal.in/aptitude/time-and-work · Last updated: 2026-09-19 · How often it appears: Very high. Reliably 2-3 questions, and pipes-and-cisterns is a near-certainty.

Every time-and-work question becomes simple once you stop thinking in days and start thinking in work-per-day. Convert each worker to a rate, add the rates, and the problem is arithmetic. Pipes and cisterns is the same topic with one rate turned negative.

## Concepts

### Work as a rate, not a duration

If A finishes a job in 10 days, A completes 1/10 of it per day. Rates add; days do not. Two people who each take 10 days finish in 5 days together, because their rates 1/10 + 1/10 = 1/5. Trying to average the days instead of the rates is the classic error.

### The LCM shortcut

Instead of fractions, set the total work equal to the LCM of the given days. If A takes 12 days and B takes 18, let total work = 36 units. Then A does 3 units/day and B does 2 units/day. All the arithmetic becomes integers, which is much faster under time pressure.

### Efficiency is inversely proportional to time

If A is twice as efficient as B, A takes half the time. So an efficiency ratio of 2:1 means a time ratio of 1:2. Questions phrased in terms of "twice as good a workman" are asking you to make this flip.

### Pipes and cisterns is the same topic

A filling pipe has a positive rate, an emptying pipe a negative one. Add them as signed rates. If the sum is negative the tank never fills — which is occasionally the intended answer.

## Formulas

| Formula | Rule | Note |
| --- | --- | --- |
| One day work | If A finishes in n days, A does 1/n per day |  |
| Two working together | Time = (a × b) / (a + b) | Where a and b are the individual times. |
| Finding the second worker | 1/b = 1/together − 1/a |  |
| Work equivalence | (M₁ × D₁ × H₁) / W₁ = (M₂ × D₂ × H₂) / W₂ | M = men, D = days, H = hours per day, W = amount of work. |
| Fill and drain together | Net rate = 1/fill − 1/empty |  |

## Worked examples

### Example 1

**Question:** A can do a job in 10 days and B in 15 days. How long do they take together?

**Solution:**

1. A does 1/10 per day, B does 1/15 per day.
2. Together = 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6 per day
3. If they do 1/6 per day, the whole job takes 6 days.

**Answer:** 6 days

**Check:** Or straight from the formula: (10 × 15) / (10 + 15) = 150 / 25 = 6.

### Example 2

**Question:** A and B together finish a job in 12 days. A alone takes 20 days. How long would B take alone?

**Solution:**

1. Together rate = 1/12. A rate = 1/20.
2. B rate = 1/12 − 1/20
3. LCM of 12 and 20 is 60: = 5/60 − 3/60 = 2/60 = 1/30
4. B does 1/30 per day.

**Answer:** B alone takes 30 days

### Example 3

**Question:** Pipe A fills a tank in 6 hours. Pipe B empties it in 8 hours. If both are opened together on an empty tank, how long until it is full?

**Solution:**

1. A fills at +1/6 per hour. B empties at −1/8 per hour.
2. Net rate = 1/6 − 1/8
3. LCM of 6 and 8 is 24: = 4/24 − 3/24 = 1/24 per hour
4. The net rate is positive, so it does fill.

**Answer:** 24 hours

**Check:** If B had been faster than A the net rate would be negative and the tank would never fill — always check the sign before answering.

## Practice questions

1. A can do a piece of work in 12 days and B in 24 days. Working together they finish in:
   - A. 6 days
   - B. 8 days
   - C. 9 days
   - D. 10 days
   - **Answer:** B. 8 days — (12 × 24) / (12 + 24) = 288 / 36 = 8 days.

2. A is twice as efficient as B. Together they finish a job in 8 days. A alone would take:
   - A. 10 days
   - B. 12 days
   - C. 14 days
   - D. 16 days
   - **Answer:** B. 12 days — Efficiency ratio 2:1 means A does 2 parts and B 1 part, 3 parts total per day. A alone needs 3/2 of the joint time = 8 × 1.5 = 12 days.

3. If 10 men complete a job in 15 days, how long will 15 men take (same rate)?
   - A. 8 days
   - B. 10 days
   - C. 12 days
   - D. 12.5 days
   - **Answer:** B. 10 days — M₁D₁ = M₂D₂ → 10 × 15 = 15 × D → D = 10 days.

4. Two pipes fill a tank in 10 hours and 15 hours respectively. Together they fill it in:
   - A. 5 hours
   - B. 6 hours
   - C. 7 hours
   - D. 8 hours
   - **Answer:** B. 6 hours — (10 × 15) / (10 + 15) = 150 / 25 = 6 hours.

5. A takes 20 days for a job. He works 5 days and leaves. B finishes the rest in 9 days. B alone would take:
   - A. 10 days
   - B. 12 days
   - C. 15 days
   - D. 18 days
   - **Answer:** B. 12 days — A completed 5/20 = 1/4. Remaining = 3/4, which B does in 9 days. So the full job takes B 9 × 4/3 = 12 days.

6. A does a job in 6 days, B in 12 days. They work together for 2 days. The fraction of work left is:
   - A. 1/4
   - B. 1/2
   - C. 1/3
   - D. 2/3
   - **Answer:** B. 1/2 — Joint rate = 1/6 + 1/12 = 3/12 = 1/4 per day. In 2 days they do 1/2. Left = 1/2.

7. A tank is filled by a pipe in 5 hours but a leak empties it in 20 hours. With both active, filling takes:
   - A. 6 hours 40 min
   - B. 6 hours
   - C. 7 hours
   - D. 8 hours
   - **Answer:** A. 6 hours 40 min — Net = 1/5 − 1/20 = 4/20 − 1/20 = 3/20 per hour → 20/3 hours = 6 hours 40 minutes.

8. If 6 workers build a wall in 8 days working 6 hours a day, how many days will 4 workers take at 8 hours a day?
   - A. 7 days
   - B. 8 days
   - C. 9 days
   - D. 10 days
   - **Answer:** C. 9 days — M₁D₁H₁ = M₂D₂H₂ → 6 × 8 × 6 = 4 × D × 8 → 288 = 32D → D = 9 days.

## Where marks get lost

- Averaging the days instead of adding the rates.
- Forgetting that an emptying pipe carries a negative rate.
- Flipping an efficiency ratio the wrong way (2:1 efficiency = 1:2 time).
- Working in fractions when the LCM method would keep everything in integers.

## Related topics

- [Time, Speed & Distance](https://www.sansal.in/aptitude/time-speed-and-distance)
- [Ratio & Proportion](https://www.sansal.in/aptitude/ratio-and-proportion)
- [Percentages](https://www.sansal.in/aptitude/percentages)

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