# Time and 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.

#### Time and Work Case (3):

Let there are three employees named K, L, and M can finish a task one by one in x, y, and z days successively. If all the three employees start working together then they can finish the task in days- $$\left[\frac{xyz}{xy + yz + zx}\right] \ days$$

Example (1): Three friends P, Q, and R can finish a task in $$5 \ days$$, $$10 \ days$$, and $$15 \ days$$, successively. If all the three friends start working together how many days they will take to finish the task?

Solution: Given values, $$x = 5 \ days$$, $$y = 10 \ days$$, and $$z = 15 \ days$$, then $$\left[\frac{xyz}{xy + yz + zx}\right]$$ $$\left[\frac{5 \times 10 \times 15}{5 \times 10 + 10 \times 15 + 15 \times 5}\right]$$ $$\left[\frac{750}{50 + 150 + 75}\right]$$ $$\left[\frac{750}{275}\right] = 2.73 \ days$$

Example (2): Two men and one women can finish a work in $$12 \ days$$, $$13 \ days$$, and $$16 \ days$$, successively. If three of them start working together, then how many days they will take to finish the work?

Solution: Given values, $$x = 12 \ days$$, $$y = 13 \ days$$, and $$z = 16 \ days$$, then $$\left[\frac{xyz}{xy + yz + zx}\right]$$ $$\left[\frac{12 \times 13 \times 16}{12 \times 13 + 13 \times 16 + 16 \times 12}\right]$$ $$\left[\frac{2496}{156 + 208 + 192}\right]$$ $$\left[\frac{2496}{556}\right] = 4.48 \ days$$

#### Time and Work Case (4):

Let there are three employees named K, L, and M. If K & L can finish a task in x days, L & M can finish the same task in y days, and M & K can finish the same task in z days, and if all the three employees start to work together, then they can finish the task in days- $$\left[\frac{2xyz}{xy + yz + zx}\right] \ days$$

Example (1): There are Three friends A, B, and C. A and B can finish a task in $$10 \ days$$, B and C can finish the same task in $$15 \ days$$, C and A can finish the same task in $$20 \ days$$. If all the three friends start working together, then how many days they will take to finish the task?

Solution: Given $$x = 10 \ days$$, $$y = 15 \ days$$, and $$z = 20 \ days$$, then $$\left[\frac{2xyz}{xy + yz + zx}\right]$$ $$\left[\frac{2 \times 10 \times 15 \times 20}{10 \times 15 + 15 \times 20 + 20 \times 10}\right]$$ $$\left[\frac{6000}{150 + 300 + 200}\right]$$ $$\left[\frac{6000}{650}\right] = 9.23 \ days$$

Example (2): A man and a women can finish a work in $$13 \ days$$, a women and a girl can finish the same work in $$17 \ days$$, and a girl and a man can finish the same work in $$14 \ days$$. If three of them start working together, then how many days they will take to finish the work?

Solution: Given $$x = 13 \ days$$, $$y = 17 \ days$$, and $$z = 14 \ days$$, then $$\left[\frac{2xyz}{xy + yz + zx}\right]$$ $$\left[\frac{2 \times 13 \times 17 \times 14}{13 \times 17 + 17 \times 14 + 14 \times 13}\right]$$ $$\left[\frac{6188}{221 + 238 + 182}\right]$$ $$\left[\frac{6188}{641}\right] = 9.6 \ days$$