Question

81. In a mixture of 40 litre, the ratio of milk and water is 4:1. If some quantity of mixture taken out and then 4 litre
9 of milk and 4 litre of water is added to the mixture then the ratio of milk and water become 8:3. Find the
quantity of mixture which was taken out initially?
A. 10 litre B. 15 litre C 12 litre
D. 18 litre
E. None of these
.​

Answer 1

Answer:

The quantity of mixture taken out initially is 15 litres

Step-by-step explanation:

Mixture = 40 litres

Amount of milk in mixture $= \frac{4}{5} \times 40 = 4 \times 8 = 32$ litres

Amount of water in mixture $= \frac{1}{5} \times 40 = 1 \times 8 = 8$ litres

Now, some quantity of mixture is taken out and then 4 litre of milk and 4 litre of water is added to the mixture, ratio of milk and water become 8 : 3

Let quantity of mixture taken out be $x$ litre

Quantity of milk in $x$ litres of mixture $=\frac{4}{5} \ times x = \frac{4x}{5}$

Quantity of water in $x$ litres of mixture $=\frac{1}{5} \ times x = \frac{x}{5}$

Now, we have

New quantity of milk $= 32 - \frac{4x}{5} + 4 = 36 - \frac{4}{5}$ litre

New quantity of water$= 8 - \frac{x}{5} + 4 = 12 - \frac{x}{5}$ litre

New Ratio = 8 : 3

We have

$\frac{36 - \frac{4x}{5}}{12 - \frac{x}{5}} = \frac{8}{3}\\\\ 3(\,36 - \frac{4x}{5})\, = 8(\,12 - frac{x}{5})\,\\\\ 108 - \frac{12x}{5} = 96 - \frac{8x}{5}\\\\ \frac{12x}{5} - \frac{8x}{5} = 108 - 96\\\\ \frac{4x}{5} = 12\\\\ x = 12 \times \frac{5}{4}\\\\ x = 3 \times 5 x = 15$

Thus, quantity of mixture taken out initially is 15 litres