Question

A barrel contains a mixture of win and water in the ratio 3:1. How much fraction of the mixture must be drawn off and substituted by water so that the ratio of wine and water in the resultant mixture in the barrel becomes 1:1

Answer 1

Answer:

1/3 fraction of the inital mixture

Step-by-step explanation:

Given, initial mixture in the barrel

Wine : Water = 3:1

Let he total volume of mixture = X

∴ Inital mixture contains

Volume of wine Ni = (3/4)X

Volume of water Ti = (1/4)X

Final mixture contains the ration of water and wine = 1:1

∴ Volume of wine in final mixture Nf = X/2

Change in volume of wine = Ni - Nf = 0.75X - 0.5X = 0.25X

∴ Mixture containing wine of actual volume 0.25X must be drawn from the initial mixture.

But Wine to water ration = 3:1

∴ When 0.25X wine is drawin, water of (0.25/3)X must be in that mixture.

∴ Total valume of mixture = 0.25 X + (0.25/3)X = (1/3) X liters.

∴ 1/3 fraction of the mixture must be drawon and substituted with water