Question

55. A mixture contains milk and water in the ratio of 5 : 1, on adding 5 litres of water, the ratio of
milk and water becomes 5:2. The quantity of milk in the original mixture is
a) 25 litres
b) 22 litres
c) 22.75 litres
32 50 litres​

Answer 1

Answer:

Step-by-step explanation:

Given:

The mixture contains milk and water in the ratio 5:1.

On adding 5 litres of water, the ratio of milk to water becomes 5:2.

To find:

The quantity of milk in the original mixture.

Solution:

The mixture contains milk and water in the ratio 5:1.

Let, the common multiple of the ratio be, 'l'.

∴ The amount of milk = (5×l)

                                  = 5l.

∴The amount of water in the mixture = (1×l)

                                                            = l

On adding 5 liters of water in the mixture, the amount of water becomes in the mixture_

(l+5)

= l+5.

On adding 5 litres of water, the ratio of milk to water becomes 5:2 .

∴ According to the problem:

5l : (l+5) = 5:2

or, (5l ×2) = 5(l+5)

or, 10l = 5l + 25

or, (10l-5l) = 25

or, 5l = 25

or, l = (25 ÷5)

or, l = 5 liters.

∴ The amount of milk in the original mixture was _

(5×5)

= 25 liters.

Answer:

           25 liters milk was there in the original mixture.

Here goes ur answer.Hope the same solves ur query.

Answer 2

In the original mixture the ratio of milk to water is 5 : 1

This means that the quantity of milk is 5 times that of water

If water is x, then milk would be 5x

According to the question,

• 5 Litres of water is added to milk
• The new ratio becomes 5 : 2

$\sf{ \frac{5x}{x + 5} = \frac{5}{2} } \\ \\ on \: cross \: multiplication \\ \\ \sf{5(x + 5) = 2(5x) } \\ \\ \implies \sf{5x + 25 = 10x} \\ \\ \implies \sf{25 = 10x - 5x} \\ \\ \implies \sf{5x = 25} \\ \\ \implies \sf{x = \frac{25}{5} } \\ \\ \therefore \boxed{ \boxed{ \bf{x = 5}}}$

$\small{ \sf{quantity \: of \: milk \: in \: original \: mixture = 5x}} \\ \\ \implies{ \sf{quantity \: of \: milk \: in \: original \: mixture =5 \times 5}} \\ = \boxed{ 25 \: litres}$

Quantity of milk = 25 Litres