SSC MTS Numerical Ability: Time and Work Shortcuts with Worked Examples

Learn the LCM (total work) method for SSC MTS time and work questions, with worked examples on pipes, efficiency and wages, common traps and a practice plan.

Time and work is one of the most predictable topics in the Numerical and Mathematical Ability part of SSC MTS & Havaldar. Once you use the LCM (total work) method, most questions become simple division. This guide explains the method, applies it to the common question types and shows how to practise on SSC MTS & Havaldar mock tests.

Check the current scheme of examination in the official notice on ssc.gov.in before you plan your preparation.

The LCM method in three steps

Take the LCM of the days given. Treat it as total work (units).
Find each person's work per day = total work ÷ their days.
Add or subtract rates as the question needs, then divide total work by the combined rate.

This avoids fractions such as 1/12 + 1/18, which is where many calculation errors happen.

Worked example 1: two people together

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

LCM(12, 18) = 36 units.
A = 36 ÷ 12 = 3 units/day. B = 36 ÷ 18 = 2 units/day.
Together = 5 units/day → 36 ÷ 5 = 7.2 days.

Worked example 2: one person leaves

A and B can do a job in 10 days, A alone in 15 days. They work together for 4 days, then A leaves. How long does B take to finish?

LCM(10, 15) = 30 units. A+B = 3/day, A = 2/day, so B = 1/day.
In 4 days: 4 × 3 = 12 units done. Remaining = 18 units.
B alone: 18 ÷ 1 = 18 days.

Worked example 3: pipes and cisterns

Pipe P fills a tank in 6 hours and pipe Q empties it in 9 hours. If both are open, how long to fill the tank?

LCM(6, 9) = 18 units. P = +3/hour, Q = −2/hour.
Net = +1/hour → 18 hours.

The emptying pipe is just a negative rate. Write the sign before you add.

Worked example 4: efficiency

A is twice as efficient as B. Together they finish a job in 8 days. How long does B take alone?

Let B = 1 unit/day, A = 2 units/day. Together = 3/day.
Total work = 3 × 8 = 24 units.
B alone = 24 ÷ 1 = 24 days.

Worked example 5: wages

A and B complete a job for ₹1,500. A alone takes 10 days and B alone 15 days. How should the money be shared?

LCM = 30. A = 3/day, B = 2/day. Wages are shared in the ratio of work done.
They work the same number of days, so the ratio is 3 : 2.
A gets ₹900, B gets ₹600.

Quick reference table

Situation	What to do
Days given for each person	LCM of days = total work
Efficiency ratio given	Use the ratio as units/day
Someone leaves or joins	Work done so far, then remaining ÷ new rate
Emptying pipe or leak	Use a negative rate
Wages	Share in the ratio of total work done

Common traps

Adding days instead of rates. 12 days + 18 days is meaningless; always add work per day.
Forgetting the sign of a leak or emptying pipe.
Mixing hours and days in the same question. Convert first.
Wages by days instead of work. Share by work done, not by the time each person takes alone.

A two-week practice plan

Days	Focus
1–3	Basic LCM questions (two and three people), 15 per day
4–5	Leaving/joining questions
6–7	Pipes, cisterns and leaks
8–9	Efficiency and wages
10–11	Timed mixed sets of 20 questions
12–14	Full mocks in the SSC MTS & Havildar series, then review every wrong answer

Review after each mock

Mark each time and work error as a method error (wrong setup), a sign error or a calculation error. Method errors need more topic practice; calculation errors need slower, written working. Track your progress across Scholareum mock tests and watch dates on the exam calendar.

Related guides

FAQs

What is the LCM method in time and work? Take the LCM of the given days as total work, find each person's work per day, then divide total work by the combined daily rate.

How do I handle a leak or emptying pipe? Treat it as a negative rate and subtract it from the filling rate.

How are wages shared in time and work questions? In the ratio of the work each person actually did.