Module 2 · SSC GD Mathematics
Time & Work
Efficiency, pipes & cisterns, alternate day work.
Efficiency · Pipes & Cisterns
Learning Objectives
- Understand the fundamental concepts of Time & Work
- Apply key formulas and techniques to solve problems
- Practice with exam-level questions to build speed and accuracy
Key Concepts
Time & Work for SSC GD & Agniveer
Time and work problems involve the relationship between workers, time, and work done. These questions appear regularly in SSC GD and Agniveer mathematics papers. The key principle is that work done = efficiency × time.
Key Concepts
Basic Principle: If A completes work in n days, A's 1-day work = 1/n. Combined work = sum of individual 1-day works. Total days = 1 / combined work. Efficiency: Efficiency is inversely proportional to time. If A takes half the time of B, A is twice as efficient. Pipes & Cisterns: Filling pipes do positive work, emptying pipes do negative work. Net rate = filling rate - emptying rate. Wages: Distributed in proportion to work done or efficiency×time.
Solved Examples
Example 1
A can do a work in 10 days, B in 15 days. How many days will they take together?
a) 5 days b) 6 days c) 7 days d) 8 days
a) 5 days b) 6 days c) 7 days d) 8 days
Solution: b) 6 days. A's 1-day = 1/10. B's 1-day = 1/15. Combined = 1/10+1/15 = 5/30 = 1/6. Total = 6 days.