Question : A can complete a work in 8 days and B can complete the same work in 11 days. How many days will they take, if both work together?
Option 1: $4 \frac{12}{17}$
Option 2: $5 \frac{12}{19}$
Option 3: $4 \frac{11}{19}$
Option 4: $4 \frac{12}{19}$
Correct Answer: $4 \frac{12}{19}$
Solution :
The rate at which A works is $\frac{1}{8}$ work per day and the rate at which B works is $\frac{1}{11}$ work per day.
Together, A and B can do $\frac{1}{8} + \frac{1}{11} = \frac{19}{88}$ work per day.
So, the time taken to complete the work when A and B work together is the reciprocal of their combined work rate = $\frac{88}{19} = 4 \frac{12}{19}$ days
Hence, the correct answer is $4 \frac{12}{19}$.
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