1. Three candles were lit simultaneously. When the first candle burned out, $\frac{2}{5}$ of the second candle remained, and $\frac{3}{7}$ of the third candle remained. What part of the third candle will remain when the second candle burns out?
# Solution

In time $t$, $\frac{3}{5}$ of the second candle and $\frac{4}{7}$ of the third candle burned.

The burning rate of the second candle is $\frac{3}{5 t}$, and the burning rate of the third candle is $\frac{4}{7 t}$.

$\frac{2}{5}$ of the second candle will burn in $\frac{2}{5} : \frac{3}{5 t} = \frac{2 t}{3}$ time.

During this time, $\frac{2 t}{3} \frac{4}{7 t} = \frac{8}{21}$ of the third candle will burn.

From the third candle, $\frac{3}{7} - \frac{8}{21} = \frac{1}{21}$ will remain.

## Criteria

A computational error or typo only in the last step of a correct solution, leading to an incorrect answer - 5 points.

Computational errors in earlier steps, resulting in an incorrect answer, with a correct approach - 3 points.