Question : Avi alone can do a piece of work in 60 days while Prakash alone can do it in 80 days. In how many days will they finish it together?
Option 1: $\frac{250}{6}$ days
Option 2: $\frac{270}{6}$ days
Option 3: $\frac{240}{7}$ days
Option 4: $\frac{140}{6}$ days
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Correct Answer: $\frac{240}{7}$ days
Solution : Let the amount of work be represented by the variable $W$. A can complete the work in 60 days. ⇒ A's work rate is $\frac{W}{60}$ per day. Prakash can complete the work in 80 days. ⇒ Prakash's work rate is $\frac{W}{80}$ per day. When they work together, their rates add up: ⇒ Combined rate = $\frac{W}{60}$ + $\frac{W}{80}$ So, the required time = $\frac{\text{Total Work}}{\text{Combined rate}}$ = $\frac{W}{\frac{W}{60}+\frac{W}{80}}$ = $\frac{1}{\frac{4+3}{240}}$ = $\frac{1}{\frac{7}{240}}$ = $\frac{240}{7}$ Hence, the correct answer is $\frac{240}{7}$ days.
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