# Positive and Negative Work 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 Positive and Negative work:

If there are two groups of workers $$x$$ and $$y$$. The group $$x$$ is working to complete a task, where as group $$y$$ is woking to destroy the task.

Here group $$x$$ is doing positive work and group $$y$$ is doing Negative work, then task will be completed $$\left[Work \ of \ group \ x - Work \ of \ group \ y\right]$$

Note: We can also use this concept in the cases of Pipes and Cistern (Tank), discussed in the next chapter.

Example (1): $$P$$ can finish a task in $$5 \ days$$, where as $$Q$$ can destroy the same task in $$10 \ days$$. If they start working at the same time then how many days it will take to complete the task.

Solution: $$P$$ can finish a task in $$5 \ days$$, so in one day $$P$$ can finish $$\frac{1}{5}$$ part of the task.

$$Q$$ can destroy the task in $$10 \ days$$, so in one day $$Q$$ can destroy $$\frac{1}{10}$$ part of the task, then $$\left[Work \ of \ P - Work \ of \ Q\right]$$ $$\left[\frac{1}{5} - \frac{1}{10}\right]$$ $$\left[\frac{2 - 1}{10}\right] = \frac{1}{10}$$

Hence task will be finish in $$10 \ days$$.

Example (2): $$Jack$$ can finish a task in $$20 \ days$$, where as $$Johnson$$ can destroy the same task in $$25 \ days$$. If they start working at the same time then how many days it will take to complete the task.

Solution: $$Jack$$ can finish a task in $$20 \ days$$, so in one day $$Jack$$ can finish $$\frac{1}{20}$$ part of the task.

$$Johnson$$ can destroy the task in $$25 \ days$$, so in one day $$Johnson$$ can destroy $$\frac{1}{25}$$ part of the task, then $$\left[Work \ of \ Jack - Work \ of \ Johnson\right]$$ $$\left[\frac{1}{20} - \frac{1}{25}\right]$$ $$\left[\frac{5 - 4}{100}\right] = \frac{1}{100}$$

Hence task will be finish in $$100 \ days$$.