Question

A mixture contains wine and water in the ratio 3 : 2 and another mixture contains them in the ratio 4: 5. How many litres of the later must be mixed with 3 litres of the former so that the resulting mixture may contain equal quantities of wine and water ??!​

Answer 1

Answer:

We have three litres of the former, so how much wine and water does it contribute to the mix? There are 3 "parts" wine and 2 "parts" water, giving us five "parts" in total, for any quantity. Since we have three litres, each part is 3 / 5 = 0.6 litres in total. Thus there are 3 x 0.6 = 1.8 litres of wine, and 2 x 0.6 = 1.2 litres of water.

Let's suppose that we add x litres of 4:5 ratio mixture. We can work out the amount of wine and water contributed by this mixture, in terms of x, in much the same way. We have 9 (= 4 + 5) parts in total, so each part consists of x / 9 litres. That means that we get 4x / 9 litres of wine, and 5x / 9 litres of water contributed by this mixture. This gives us, in our resultant mixture, the quantities:

4x / 9 + 1.8 litres of wine

5x / 9 + 1.2 litres of water

Now, since the mixture is supposed to be equal quantities, we need:

4x / 9 + 1.8 = 5x / 9 + 1.2

x / 9 = 0.6

x = 5.4

Thus, we need 5.4 litres of the latter solution to achieve parity.