# Time and Work: Case - 1 & 2

Case (1): Let a employee named M can finish a task in x days, and another employee named N can finish the same task in y days. If both employees start working together then they can complete the task in days- $$\left[\frac{xy}{x + y}\right] days$$

Example (1): A man can finish a task in $$15 \ days$$ and a women can finish the same task in $$20 \ days$$. If Both start working together then how many days they will take to finish the task?

Solution: Given values, $$x = 15 \ days$$ and $$y = 20 \ days$$, then $$\left[\frac{xy}{x + y}\right] \ days$$ $$\left[\frac{15 \times 20}{15 + 20}\right] \ days$$ $$\left[\frac{300}{35}\right] = 8.57 \ days$$

Example (2): Mr.John can finish a task in $$5 \ days$$ and Mr.Jack can finish the same task in $$6 \ days$$. If Both start working together then how many days they will take to finish the task?

Solution: Given values, $$x = 5 \ days$$ and $$y = 6 \ days$$, then $$\left[\frac{xy}{x + y}\right] \ days$$ $$\left[\frac{5 \times 6}{5 + 6}\right] \ days$$ $$\left[\frac{30}{11}\right] = 2.73 \ days$$

Case (2): Let two employees M and N together can finish a task in x days. If only M works alone, he can finish the task in y days then employee N can finish the same task alone in days- $$\left[\frac{xy}{x - y}\right] days$$

Example (1): Two friends P and Q together can finish a task in $$10 \ days$$, if P alone can finish the same task in $$5 \ days$$, then how many days Q alone needs to finish the same task?

Solution: Given values, $$x = 10 \ days$$, $$y = 5 \ days$$, then $$\left[\frac{xy}{x - y}\right] \ days$$ $$\left[\frac{10 \times 5}{10 - 5}\right] \ days$$ $$\left[\frac{50}{5}\right] = 10 \ days$$

Example (2): A man and a women, together can finish a task in $$25 \ days$$, if the man alone can finish the same task in $$12 \ days$$, then find how many days the women alone needs to finish the same task?

Solution: Given values, $$x = 25 \ days$$, $$y = 12 \ days$$, then $$\left[\frac{xy}{x - y}\right] \ days$$ $$\left[\frac{25 \times 12}{25 - 12}\right] \ days$$ $$\left[\frac{300}{13}\right] = 23.07 \ days$$