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 $$ \left[\frac{xy}{x - y}\right] \ days $$ $$ \left[\frac{25 \times 12}{25 - 12}\right] \ days $$ $$ \left[\frac{300}{13}\right] = 23.07 \ days $$