3 Simple Shortcut Tricks to Solve Time and Work Problems
Are you preparing for competitive exams like RRB, SSC, or Bank PO? Time and Work is one of the most important topics in Quantitative Aptitude. While traditional methods can be time-consuming, using shortcuts can help you solve problems in seconds.
The Problem: If A can complete a work in 12 days and B can complete the same work in 24 days, how many days will it take for A and B to complete the work together?
Method 1: The Direct Formula
This is the fastest method when you only have two people (A and B).
Formula: Total Days = (x * y) / (x + y)
- x: 12 days (A's time)
- y: 24 days (B's time)
- Calculation: (12 * 24) / (12 + 24) = 288 / 36 = 8 Days
Method 2: The LCM Method
The LCM method is highly recommended because it works perfectly even when three or more people (A, B, and C) are involved.
- Find Total Work: LCM of 12 and 24 = 24 units.
- Calculate Efficiency (Work per day):
- A's efficiency: 24 / 12 = 2 units/day
- B's efficiency: 24 / 24 = 1 unit/day
- Combined Efficiency: 2 + 1 = 3 units/day.
- Final Answer: 24 / 3 = 8 Days.
Method 3: The Efficiency Ratio Method
This method focuses on the relationship between time and speed (efficiency).
- Time Ratio (A:B): 12 : 24 → 1 : 2
- Efficiency Ratio: Inverse of time ratio → 2 : 1
- Total Work Calculation: (A's Efficiency 2) * (A's Days 12) = 24 total parts.
- Combined Time: 24 / (2 + 1) = 8 Days.
