Time and Work Problems — Shortcuts for Placement Exams

Time and Work Problems — Shortcuts for Placement Exams

Time and work is a consistently tested topic in aptitude for placements. These problems test your ability to understand work rates and combine them intelligently. The LCM method makes these problems significantly faster than the traditional fraction method and is the preferred approach for all placement tests under time pressure.

The LCM Method

Assign total work a value equal to the LCM of all the given number of days. This converts all fractional rates into whole numbers, eliminating messy fractions entirely. If A finishes in 12 days and B in 18 days, set total work to 36 (LCM of 12 and 18). A completes 3 units per day and B completes 2 units per day. Together they complete 5 units per day, finishing in 36 divided by 5, which is 7.2 days.

Solved Example

A can do work in 12 days and B in 18 days. They work together for 4 days, then A leaves. How many more days does B need? Total work equals 36 units. Together they complete 5 times 4, which is 20 units. Remaining work equals 36 minus 20, which is 16 units. B alone finishes 16 divided by 2, which is 8 days. Answer: 8 more days.

Pipes and Cisterns

Pipe problems use identical logic. Inlet pipes have positive rates because they fill the tank. Outlet pipes have negative rates because they drain it. If an inlet fills in a hours and an outlet drains in b hours with both open, net fill time equals ab divided by b minus a, provided b is greater than a. If the drain is faster, the tank will never fill.

Interview Tips

Once you set total work equal to the LCM of given days, all calculations become simple integers. Practice this method until it is automatic. Pipe and cistern problems are simply time-work problems with positive and negative rates — apply the exact same approach and you will solve both types with equal ease.