Question

a mixture contains milk and water in the ratio of 5:3.if 16 litres of mixture is taken out and 16 litres of water added to it and ratio of milk and waterbecomes 3:5.find the initial quantity of water in the mixture.

Answer 1

Let the initial amount of milk be x and water be y

According to the question $\frac{x}{y} = \frac{5}{3}$

Or, $x = \frac{5}{3}y$ ... eq(i)

As the mixture is composed of water and milk, thus we can write :-

Mixture = milk + water

M = x + y

Now 16 litres of mixture is taken out ...

We can say that $\frac{5}{5+3}\times 16$ of milk is taken out and $\frac{3}{5+3}\times 16$ of water is taken out

Thus the new mixture becomes :-

M = (x-10) + (y-6)

Now in this mixture, 16 litres of water is added. Thus new mixture becomes :

M = (x-10) + (y-6+16)

M = (x-10) + (y+10)

Now according to the question, this mixture has the ratio of 3 : 5

$\therefore \frac{x-10}{y+10} = \frac{3}{5}$

$5x - 50 = 3y + 30$

$x = \frac{3y+80}{5}$ ... eq(ii)

Comparing x from eq(i) and eq(ii)

$\frac{5y}{3} = \frac{3y+80}{5}$

$\frac{25y}{3} = 3y + 80$

$\frac{25y - 9y}{3} = 80$

$\frac{16y}{3} = 80$

$y = \frac{80 \times 3}{16}$

$y = 15$

Thus the initial amount of water is 15 litres.