Question : A alone can do $\frac{1}{4}$th part of the work in 12 days. B alone can do $\frac{1}{5}$th part of the work in 4 days. In how many days can A and B together can do the same work?
Option 1: $\frac{330}{13}$ days
Option 2: $\frac{240}{17}$ days
Option 3: $\frac{210}{4}$ days
Option 4: $\frac{255}{7}$ days
Correct Answer: $\frac{240}{17}$ days
Solution :
Let the total work as 1 unit.
Given that A alone can do $\frac{1}{4}$th part of the work in 12 days.
The rate at which A works $= \frac{1}{12×4} = \frac{1}{48}$
And given that B alone can do $\frac{1}{5}$th part of the work in 4 days.
The rate at which B works $= \frac{1}{4×5} = \frac{1}{20} $
When A and B work together, their combined rate $ = \frac{1}{48} + \frac{1}{20} = \frac{17}{240} $
Therefore, the time it takes for A and B to finish the work together $= \frac{1}{\frac{17}{240}} = \frac{240}{17} $
Hence, the correct answer is $\frac{240}{17} $ day.
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