Question : A and B together can complete a given work in 10 days. C can complete the same work alone in 15 days. In how many days can they complete the work, if all three work together?
Option 1: 8 days
Option 2: 5 days
Option 3: 6 days
Option 4: 10 days
Correct Answer: 6 days
Solution :
1 day's work of A and B = $\frac{1}{10}$
1 day's work of C = $\frac{1}{15}$
1 day's work of A, B and C together = $\frac{1}{10}+\frac{1}{15}
= \frac{3+2}{30}
= \frac{1}{6}$
Thus, the work is completed in 6 days.
Hence, the correct answer is 6 days.
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