Question

There are three bottles of mixture of syrup and water in the ratios $2 : 3$, $3 : 4$ and $7 : 5$. 10 litres of first and 21 litres of second bottles are taken. How much quantity of mixtures from third bottle is to be taken so that the final syrup and water ratio of mixture from three bottles will be $1 : 1$ if the final mixture from all the three bottles is added and mixed in a big container?

Accepted Answer

C. In bottle 1 (10 litres, ratio 2:3): - Syrup = $\frac{2}{5} 	imes 10 = 4$ litres - Water = $6$ litres In bottle 2 (21 litres, ratio 3:7): - Syrup = $\frac{3}{7} 	imes 21 = 9$ 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 = $12x = 12 	imes 2.5 = 30$ litres.

Mixing Three Bottles of Syrup and Water

Explanation

Practise this under exam conditions