Mixing Three Bottles of Syrup and Water

In bottle 1 (10 litres, ratio 2:3):

• Syrup = $\frac{2}{5} \times 10 = 4$ litres
• Water = $6$ litres

In bottle 2 (21 litres, ratio 3:7):

• Syrup = $\frac{3}{7} \times 21 = 9$ litres
• Water = $12$ litres

Let $12x$ litres be taken from bottle 3 (ratio 7:5):

• Syrup = $7x$ litres
• Water = $5x$ litres

Total Syrup = $4 + 9 + 7x = 13 + 7x$ Total Water = $6 + 12 + 5x = 18 + 5x$

Since the final ratio of syrup to water is $1 : 1$: $13 + 7x = 18 + 5x \implies 2x = 5 \implies x = 2.5$

Quantity taken from third bottle = $12x = 12 \times 2.5 = 30$ litres.