Question : A can do a job in 10 days and B can do the same job in 15 days. They start working together, but B leaves after 5 days. How many more days does A want to finish the work?
Option 1: $2$ days
Option 2: $1\frac{2}{3}$ days
Option 3: $3$ days
Option 4: $2\frac{2}{3}$ days
Correct Answer: $1\frac{2}{3}$ days
Solution :
Given: A can do a job in 10 days.
So, work done by A in 1 day = $\frac{1}{10}$
B can do the same job in 15 days.
So, work done by B in 1 day = $\frac{1}{15}$
They start working together, but B leaves after 5 days.
Work done by A and B together in 1 day = $\frac{1}{10}+\frac{1}{15}=\frac{1}{6}$
Work done by A and B together in 5 days = $5×\frac{1}{6}=\frac{5}{6}$
Remaining work = $1-\frac{5}{6}=\frac{1}{6}$
So, A does the remaining work in $10×\frac{1}{6}=\frac{5}{3}=1\frac{2}{3}$ days.
Hence, the correct answer is $1\frac{2}{3}$ days.
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