# Concept of Efficiency Aptitude Formulas, Definitions, & Examples:

#### Overview:

 Topic Included: Formulas, Definitions & Exmaples. Main Topic: Quantitative Aptitude. Quantitative Aptitude Sub-topic: Time and Work Aptitude Notes & Questions. Questions for practice: 10 Questions & Answers with Solutions.

#### Concept of Efficiency:

Work efficiency (ability to do any work) of any person is inversely proportional to time.$$Efficiency \propto \frac{1}{Time}$$

Example (1): The efficiency of worker P is twice than the worker Q. If P can finish a task before $$10 \ days$$ than Q, then find how many days P needs to finish the task?

Solution: Let P can finish the task in $$x \ days$$ and Q can finish the task in $$2x \ days$$, but P can finish the task $$10 \ days$$ before Q then, $$2x - x = 10$$ $$x = 10 \ days$$
P can finish the task in $$x \ days = 10 \ days$$ and Q can finish the task in $$2x \ days = 20 \ days$$.

Example (2): The efficiency of a man is thrice than a women. If the man can finish a task before $$6 \ days$$ than the women, then find how many days the man needs to finish the task?

Solution: Let the man can finish the task in $$x \ days$$ and women can finish the task in $$3x \ days$$, but the man can finish the task $$6 \ days$$ before the women then, $$3x - x = 6$$ $$x = 3 \ days$$
the man can finish the task in $$x \ days = 3 \ days$$ and the women can finish the task in $$3x \ days = 3 \times 3 = 9 \ days$$.

Example (3): P is two times as efficient as Q and finish a work $$16 \ days$$ before Q, then find how many days required to finish the work if both are working simultaneously?

Solution: Let P can finish the work in $$x \ days$$ and Q can finish the work in $$2x \ days$$, then $$2x - x = 6$$ $$x = 6 \ days$$ $$2x = 12 \ days$$ together they can finish the work, $$\frac{1}{6} + \frac{1}{12}$$ $$= \frac{3}{12} = \frac{1}{4}$$ Hence they need $$4 \ days$$ to finish the work.