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
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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