Question : P, Q, and R can complete a piece of work in 10 days, 15 days, and 20 days, respectively. If they work together, in how many days can they finish the same work?
Option 1: $4 \frac{8}{13}$
Option 2: $4 \frac{3}{7}$
Option 3: $4 \frac{7}{13}$
Option 4: $4 \frac{5}{7}$
Correct Answer: $4 \frac{8}{13}$
Solution :
P, Q and R can complete a task in 10 days, 15 days and 20 days, respectively.
P's work in 1 day = $\frac{1}{10}$
Q's work in 1 day = $\frac{1}{15}$
R's work in 1 day = $\frac{1}{20}$
Work done by P, Q, and R together in 1 day = $\frac{1}{10}+\frac{1}{15}+\frac{1}{20} = \frac{13}{60}$
So, P, Q, and R can complete the whole task in $\frac{60}{13}$ days = $4 \frac{8}{13}$ days
Hence, the correct answer is $4 \frac{8}{13}$ days.
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