Question : A can do a piece of work in 5 days and B in 4 days. How long will they take to do the same work when working together?
Option 1: $9$ days
Option 2: $2\frac{2}{9}$ days
Option 3: $4\frac{1}{3}$ days
Option 4: $3\frac{2}{9}$ days
Correct Answer: $2\frac{2}{9}$ days
Solution :
Given: A can do a piece of work in 5 days and B in 4 days.
If a man can do the work in $n$ days, then one day's work of the man $=\frac{1}{n}$.
1 day work of A $=\frac{1}{5}$
1 day work of B $=\frac{1}{4}$
1 day work of (A + B) together $=\frac{1}{5} + \frac{1}{4}=\frac{4+5}{20} = \frac{9}{20}$
So, (A + B) together can complete the work in $=\frac{20}{9} = 2\frac{2}{9}$ days
Hence, the correct answer is $2\frac{2}{9}$ days.
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