CareerKit

Time and Work Shortcuts: The LCM Method with 6 Solved Examples

Solve time and work aptitude questions faster with the LCM method. Six solved examples: two workers, pipes and cisterns, leaving midway and efficiency.

By the CareerKit team · · 5 min read

Time and work is a standard topic in the quantitative section of placement aptitude tests, and it's very scoreable once you stop using fractions. The fastest approach is the LCM method, also called the total work method.

This post explains the method, then solves six common question types step by step. Every answer below was checked by calculation.

The LCM method in three steps

The usual approach is "A does 1/12 of the work per day, B does 1/18..." and then adding fractions. It works, but it's slow and easy to get wrong under time pressure. The LCM method avoids fractions completely:

  1. Assume the total work is the LCM of the given days. This gives a whole number of "units".
  2. Find each person's work per day by dividing the total work by their days.
  3. Answer with simple division: time = work ÷ rate.

Example 1: Two people working together

Question: A can finish a job in 12 days and B in 18 days. How long will they take working together?

  • Total work = LCM(12, 18) = 36 units
  • A's rate = 36 ÷ 12 = 3 units/day
  • B's rate = 36 ÷ 18 = 2 units/day
  • Together = 3 + 2 = 5 units/day
  • Time = 36 ÷ 5 = 7.2 days, which is 7 1/5 days

Answer: 7 1/5 days.

Example 2: Finding one person's time

Question: A and B together finish a job in 10 days. A alone takes 15 days. How long will B take alone?

  • Total work = LCM(10, 15) = 30 units
  • A + B together = 30 ÷ 10 = 3 units/day
  • A alone = 30 ÷ 15 = 2 units/day
  • So B = 3 − 2 = 1 unit/day
  • B alone = 30 ÷ 1 = 30 days

Answer: 30 days.

Example 3: Pipes and cisterns

Pipes are the same idea, except an outlet pipe has a negative rate.

Question: Pipe A fills a tank in 20 minutes and pipe B fills it in 30 minutes. Pipe C empties the full tank in 15 minutes. If all three are opened together, how long does it take to fill the empty tank?

  • Tank capacity = LCM(20, 30, 15) = 60 units
  • A = 60 ÷ 20 = +3 units/min
  • B = 60 ÷ 30 = +2 units/min
  • C = 60 ÷ 15 = −4 units/min (it empties)
  • Net = 3 + 2 − 4 = +1 unit/min
  • Time = 60 ÷ 1 = 60 minutes

Answer: 60 minutes (1 hour).

Example 4: One person leaves midway

Question: A can do a job in 10 days and B in 15 days. They work together for 4 days, then A leaves. How many more days will B take to finish the job?

  • Total work = LCM(10, 15) = 30 units
  • A = 3 units/day, B = 2 units/day, together 5 units/day
  • In 4 days together they finish 4 × 5 = 20 units
  • Work left = 30 − 20 = 10 units
  • B alone needs 10 ÷ 2 = 5 more days

Answer: 5 more days (9 days in total from the start). Read the question carefully: "how many more days" and "total days" are different answers, and both are usually in the options.

Example 5: Efficiency questions

Question: A is twice as efficient as B. Together they finish a job in 12 days. How long would each take alone?

Here you don't know the days, so take the efficiency ratio as the rates:

  • A = 2 units/day, B = 1 unit/day, together 3 units/day
  • Total work = 3 × 12 = 36 units
  • A alone = 36 ÷ 2 = 18 days
  • B alone = 36 ÷ 1 = 36 days

Answer: A takes 18 days, B takes 36 days.

Example 6: More people, fewer days (man-days)

Question: 12 workers can build a wall in 10 days. How many days would 8 workers take?

Use the man-days rule: the total work in "worker-days" stays the same. M1 × D1 = M2 × D2.

  • Total work = 12 × 10 = 120 worker-days
  • With 8 workers: 120 ÷ 8 = 15 days

Answer: 15 days. Fewer workers, more days: if your answer goes the other way, check the multiplication. If the question also changes the hours per day, extend the rule to M1 × D1 × H1 = M2 × D2 × H2.

A checklist for the exam

  • Write the total work (the LCM) first, then every rate, before doing anything else.
  • Give outlet pipes and "work that is undone" a negative rate.
  • For "efficiency" or "ratio" questions, use the ratio itself as the rates.
  • For "leaves after X days" questions, subtract the work already done, then divide the rest.
  • Re-read whether the question asks for "more days" or "total days".

Practise more

Time and work is one topic in the quantitative section, alongside percentages, profit and loss, ratios, time-speed-distance and number series. You can read more solved questions free on our aptitude questions page.