Question : P and Q together complete a job in $4 \frac{2}{5}$ days. R and S complete the same job in $4 \frac{8}{9}$ days. If P, Q, R, and S work together, how many days do they need to complete the same job?
Option 1: $2 \frac{7}{18}$
Option 2: $1 \frac{7}{18}$
Option 3: $1 \frac{6}{19}$
Option 4: $2 \frac{6}{19}$
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Correct Answer: $2 \frac{6}{19}$
Solution :
P and Q complete the job in $4 \frac{2}{5}$ days = $\frac{22}{5}$ days
R and S complete the same job in $4 \frac{8}{9}$ days = $\frac{44}{9}$ days
P, Q, R, and S, working together, would complete in 1 day $=\frac{5}{22}+ \frac{9}{44} = \frac{10+9}{44} = \frac{19}{44}$th of the job.
$\therefore$ P, Q, R, and S would complete the entire job in $\frac{44}{19} = 2\frac{6}{19}$ days
Hence, the correct answer is $2\frac{6}{19}$ days.
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