To complete a work, Aditi takes 60% more time than Bimla. If both of them work together, they take 16 days to complete the work. How much time shall Bimla take to do it alone?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 26 days
In time-and-work questions, a person who finishes a job in \(n\) days does \(\frac{1}{n}\) of it in one day, and when two people work together their one-day work is added.
The two times (Aditi takes 60% more):
Let Bimla take \(x\) days
Aditi takes \(1.6x=\frac{8x}{5}\) days
Working together (together they finish in 16 days):
One-day work together: \(\displaystyle \frac{1}{x}+\frac{5}{8x}=\frac{13}{8x}\)
\(\displaystyle \frac{13}{8x}=\frac{1}{16}\)
\(8x=13\times16=208\)
\(x=26\) days