| 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. |
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 $$ \left[\frac{xyz}{xy + yz + zx}\right] $$ $$ \left[\frac{12 \times 13 \times 16}{12 \times 13 + 13 \times 16 + 16 \times 12}\right] $$ $$ \left[\frac{2496}{156 + 208 + 192}\right] $$ $$ \left[\frac{2496}{556}\right] = 4.48 \ days $$
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 $$ \left[\frac{2xyz}{xy + yz + zx}\right] $$ $$ \left[\frac{2 \times 13 \times 17 \times 14}{13 \times 17 + 17 \times 14 + 14 \times 13}\right] $$ $$ \left[\frac{6188}{221 + 238 + 182}\right] $$ $$ \left[\frac{6188}{641}\right] = 9.6 \ days $$