Concept of Efficiency Aptitude Formulas, Definitions, & Examples:

Overview:

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.