Question : A, B, and C working alone, can complete a job in 16, 24, and 36 days, respectively. In how many days can they complete the job if they work together?
Option 1: $7 \frac{11}{19}$
Option 2: $5 \frac{17}{19}$
Option 3: $4 \frac{13}{19}$
Option 4: $6 \frac{7}{19}$
Correct Answer: $7 \frac{11}{19}$
Solution :
Given: A, B, and C working alone, can complete a job in 16, 24, and 36 days.
1 day work of A = $\frac{1}{16}$
1 day work of B = $\frac{1}{24}$
1 day work of C = $\frac{1}{36}$
1 day work of A + B + C = $\frac{1}{16}+\frac{1}{24}+\frac{1}{36}$
= $\frac{9+6+4}{144}=\frac{19}{144}$
When they work together, they will finish the work in $\frac{144}{19}=7\frac{11}{19}$ days.
Hence, the correct answer is $7\frac{11}{19}$.
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