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?

In bottle 1 (10 l), syrup and water is in the ratio 2 : 3

So, amount of syrup = 4l and amount of water = 6l.

In bottle 2 (21 l), syrup and water is in the ratio 3 : 4

So, amount of syrup = 9l and amount of water = 12l.

Let, say $$12x$$ l of solution is taken from bottle 3.

So, amount of syrup = $$7x$$ l and amount of water = $$5x$$ l.

So, total amount of syrup = $$4+9+7x=13+7x$$

Total amount of water = $$6+12+5x=18+5x$$ l.

Now, final ratio of syrup and water is 1 : 1

So, $$13+7x=18+5x$$

or, $$7x-5x=18-13$$

or, $$2x=5$$

or, $$x=\dfrac{5}{2}$$

So, amount from third bottle = $$12x=12\times\ \dfrac{5}{2}=30$$ litres.