1+ [ Problems on percentages and ratios ]

Vasya borrowed a book from a friend for three days. On the first day, he read half of the book, on the second day — a third of the remaining pages, and on the third day, he read half of what he read in the first two days. Did Vasya manage to finish the book in three days?

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What part of the book did Vasya read on the second day

## Solution

On the first day, Vasya read $\frac{1}{2}$, on the second day $\frac{1}{3}$ of $\left(1-\frac{1}{2}\right)$, i.e., $\frac{1}{6}$. Therefore, in the first 2 days, Vasya read $\left(\frac{1}{2}+\frac{1}{6}\right)=\frac{2}{3}$ of the book; hence, on the third day, he read the remaining $\frac{1}{3}$ of the book, meaning he managed to read the entire book in 3 days.

## Answer

Yes.