Question : A can do one and a half as much work as B can do in one day. B alone can do a piece of work in 18 days. They together can finish that work in:
Option 1: $10\frac{1}{5}$ days
Option 2: $11\frac{1}{5}$ days
Option 3: $5\frac{1}{5}$ days
Option 4: $7\frac{1}{5}$ days
Correct Answer: $7\frac{1}{5}$ days
Solution :
Given: Time taken by B = 18 days
B's one day work = $\frac{1}{18}$
A's one day work = $1\frac{1}{2}$ of B's
= $\frac{3}{2}×\frac{1}{18}$ = $\frac{3}{36}$ = $\frac{1}{12}$
So, (A+B)'s one day work = $\frac{1}{12}+\frac{1}{18}$
= $\frac{3+2}{36}$ = $\frac{5}{36}$
So, the time taken by A and B together to finish the work = $\frac{36}{5}$ = $7\frac{1}{5}$
Hence, the correct answer is $7\frac{1}{5}$ days.
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