## 3. Disinfection

Family Ecological, upon entering the apartment, has a bottle of disinfectant that, of course, they make themselves. The mother poured out $\frac{3}{5}$ of the total amount and transferred it to her bottle. Then the father poured out $\frac{1}{6}$ of the remainder into his bottle. After that, the son poured $\frac{6}{7}$ of the remainder into his bottle, but he spilled $15 \mathrm{ml}$. After that, only $10 \mathrm{ml}$ of liquid remained in the bottle. How many milliliters of disinfectant were in the bottle at the beginning?

Result: $\quad 525$
## Solution, first method.

Since there are $10 \mathrm{ml}$ left in the bottle, and the son spilled $15 \mathrm{ml}$, it means that $25 \mathrm{ml}$ remained in the bottle after the son took his share. Since the son took $\frac{6}{7}$ of the liquid remaining in the bottle after the father's share, $25 \mathrm{ml}$ represents $\frac{1}{7}$ of the liquid remaining after the father's share.

We conclude: after the father's share, $7 \cdot 25=175 \mathrm{ml}$ of liquid remained in the bottle.

The father consumed $\frac{1}{6}$ of the liquid remaining in the bottle after the mother's share, so $175 \mathrm{ml}$ represents $\frac{5}{6}$ of the liquid remaining in the bottle after the mother's share.

If $\frac{5}{6}$ of the liquid is $175 \mathrm{ml}$, then $\frac{1}{6}$ of the liquid is $175: 5=35 \mathrm{ml}$.

We conclude: after the mother's share, $6 \cdot 35=210 \mathrm{ml}$ of liquid remained in the bottle.

The mother consumed $\frac{3}{5}$ of the liquid in the bottle, leaving $\frac{2}{5}$ of the liquid.

Finally, if $\frac{2}{5}$ of the liquid in the bottle is $210 \mathrm{ml}$, then $\frac{1}{5}$ of the liquid is $210: 2=105 \mathrm{ml}$, so the bottle originally contained $5 \cdot 105=525 \mathrm{ml}$ of disinfectant liquid.

Solution, second method.

Let $x$ be the amount of disinfectant liquid in the bottle at the beginning, in ml.

After the mother poured out her share, $\frac{2}{5} x$ of the liquid remained. Since the father poured out $\frac{1}{6}$ of the remainder, i.e., $\frac{1}{6} \cdot \frac{2}{5} x=\frac{1}{15} x$ of the liquid, a total of $\left(\frac{3}{5}+\frac{1}{15}\right) x=\frac{10}{15} x=\frac{2}{3} x$ of the liquid was poured out, leaving $\frac{1}{3} x$ of the liquid.

Since the son poured out $\frac{6}{7}$ of the remainder, i.e., $\frac{6}{7} \cdot \frac{1}{3} x=\frac{2}{7} x$ of the liquid, a total of $\left(\frac{2}{3}+\frac{2}{7}\right) x=\frac{20}{21} x$ of the liquid was poured out. $\frac{1}{21} x$ of the liquid remained. Since $10 \mathrm{ml}$ remained in the bottle and the son spilled $15 \mathrm{ml}$, it means that $25 \mathrm{ml}$ remained in the bottle after the son took his share.

Therefore, from $\frac{1}{21} x=25 \mathrm{ml}$, it follows that $x=525 \mathrm{ml}$.