Question : A can do a piece of work alone in 40 days. A and B together can do the same work in 10 days. C is 50% less efficient than B. In how many days can A and C together complete the same work?
Option 1: 20 days
Option 2: 24 days
Option 3: 16 days
Option 4: 12 days
Correct Answer: 16 days
Solution :
According to the question
(A + B)'s 1 day work = $\frac{1}{10}$
A's 1 day work = $\frac{1}{40}$
⇒ B's 1 day work = $\frac{1}{10}$ – $\frac{1}{40}$ = $\frac{3}{40}$
Now, C's 1 day work = $\frac{1}{2}$ of B's 1 day work = $\frac{3}{80}$
⇒ (A + C)'s 1 day work = $\frac{1}{40}$ + $\frac{3}{80}$ = $\frac{5}{80}$
⇒ Time taken by A and C together = $\frac{1}{Rate}$ = $\frac{1}{\frac{5}{80}}$ = $\frac{80}{5}$ = 16
Hence, the correct answer is 16 days.
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