BeginnerIn-depth3 min readUpdated 30 Sept 2026

How do you solve time and work problems quickly?

SHORT ANSWER

Convert each person's time into work per day (1 divided by days), add rates when people work together, and divide total work by the combined rate. The LCM method makes it faster. Take total work as the LCM of the days, so each rate becomes a whole number.

Explain it simply

If Ravi paints a wall in 10 days, he paints one tenth of it each day. If Priya paints it in 15 days, she paints one fifteenth each day. Together they paint 1/10 + 1/15 = 1/6 of the wall per day, so they finish in 6 days. Every time and work question is about rates: how much work per day, not how many days.

Example

Question: A can finish a job in 12 days, B in 18 days. They work together for 4 days, then A leaves. How long does B take to finish the rest?

LCM method:

Total work = LCM(12, 18) = 36 units.
A's rate = 36 / 12 = 3 units per day. B's rate = 36 / 18 = 2 units per day.
Together for 4 days: (3 + 2) x 4 = 20 units done.
Left: 36 - 20 = 16 units. B alone: 16 / 2 = 8 days.

A quick check in code:

const total = 36;          // LCM of 12 and 18
const a = total / 12;      // 3 units a day
const b = total / 18;      // 2 units a day
const left = total - (a + b) * 4;
console.log(left / b); // Output: 8

How it works

Work = Rate x Time. If a person does a job in n days, their rate is 1/n of the job per day.
Working together: add the rates. Working against (like a leak emptying a tank): subtract.
Efficiency: if A is twice as efficient as B, A takes half the time.
Man-days: M1 x D1 x H1 / W1 = M2 x D2 x H2 / W2, where M is men, D is days, H is hours per day and W is work. Use this for "20 men build a wall in 10 days" type questions.
Pipes and cisterns are the same idea: filling pipes add, emptying pipes subtract.

Real-world use

These questions appear in almost every placement aptitude test (TCS NQT, Infosys, Wipro, Accenture, AMCAT, bank exams). The same rate thinking also helps in real project planning: if one developer finishes a feature in 6 days, two developers do not always finish it in 3, because communication has a cost.

Common mistakes

Adding days instead of rates: 10 days + 15 days is not the answer to anything.
Forgetting to subtract the leak or emptying pipe.
Mixing units: some questions give hours per day, and you must multiply them in.
Not re-reading who leaves when in "A leaves after 4 days" questions.

What to say in the interview

In an aptitude round nobody asks you to explain, but in a panel discussion say: "I convert each person's time into a rate, take the LCM of the days as total work so the rates are whole numbers, add or subtract rates depending on whether they help or work against each other, then divide the remaining work by the combined rate."

Follow-up questions

Pipe A fills a tank in 6 hours and pipe B empties it in 9 hours. How long to fill it with both open?
A and B together take 8 days, and A alone takes 12. How long does B take alone?
If 15 men build a wall in 20 days working 8 hours a day, how long do 20 men take working 6 hours a day?

Go deeper

Read these once the basics above feel easy.

Answers to the follow-ups: tank = 18 hours (LCM 18, rates +3 and -2, so 18 / 1). B alone = 24 days (LCM 24, together 3, A 2, B 1). Wall = 20 days (15 x 20 x 8 = 20 x D x 6, so D = 20).

#aptitude #time-and-work #quantitative