Question : A can do $\frac{2}{5}$ of a work in 6 days and B can do $\frac{2}{3}$ of the same work in 12 days. A and B worked together for 6 days. C alone completed the remaining work in 8 days. A and C, working together, will complete the same work in:
Option 1: 9 days
Option 2: 12 days
Option 3: 10 days
Option 4: 8 days
Correct Answer: 10 days
Solution :
A does $\frac{2}{5}$ of a work in 6 days.
One day work of A = $\frac{2}{5×6}$ = $\frac{1}{15}$
B can do $\frac{2}{3}$ of the same work in 12 days.
One day work of B is $\frac{2}{3×12}$ = $\frac{1}{18}$
Work done in 6 days if A and B worked together = $6\times (\frac{1}{15}+\frac{1}{18})$
= $6\times\frac{11}{90}$
= $\frac{11}{15}$
Remaining work = $1-\frac{11}{15}$ = $\frac{4}{15}$
C alone completed the remaining work i.e. $\frac{4}{15}$ of the work in 8 days
So, One day work of C = $\frac{4}{15×8}$ = $\frac{1}{30}$
1-day work of A and C = $\frac{1}{15}+\frac{1}{30}$ = $\frac{2+1}{30}$ = $\frac{1}{10}$
Thus, the work is completed by A and C in 10 days.
Hence, the correct answer is 10 days.
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