## Ratio Example 4

**Example 1 :**

Milk and water in the ratio 5 : 3 is contain in a 20 litres of mixture . If 4 litres of this mixture be replaced by 4 litres of milk , the ratio of milk to water in the new mixture would be ?

**Answer :**

Quantity of milk in a mix = ( 16 x 5 / 8 ) = 10 litres .

quantity of milk in 20 litres of new mix = ( 10 + 4 ) = 14 litres .

quantity of water in it ( 20 – 14 ) = 6 litres.

Ratio of milk and water in the new ratio mix is = 14 : 6 = 7 : 3

**Example 2:**

In a bottle mixture of 80 liters and the ratio of milk and water is 3 : 2. If this mixture ratio is to be 2 : 3. What the quantity of water to be further added ?

**Answer :**

Step 1: Quantity of Milk ( 80 x 3 / 5 ) = 48 liters, So Quantity of water in it ( 80 – 48 ) = 32 liters.

Step 2: New Ratio required 2 : 3, Let x water to be added, Then Milk : Water is = 48 : (32+x)

=48 / (32 + x).

Step 3: Now 48 / (32 + x) = 2 : 3

48 / (32 + x) = 2 / 3

2x = 144 – 64

x = 80/2

=40 liters.

**Example 3 :**

The ratio of copper and zinc is 9 : 3 in an alloy . If quantity of zinc is 24 kg. the quantity of copper is would be ?

**Answer :**

ratio of copper and zinc is 9 : 3

Let the required quantity of copper be x kg.

So, 9 : 3 : 24 : x

9x = 24 x 3

x = 72 / 9

x = 8 kg

**Example 4 :**

The ratio between the number of men and women in a society is 31 : 23 , When 75 more women are added in the society, this ratio becomes 124 : 107 . How many more women should be added in the society in order to make the number of men and women be equal?

**Answer :**

31x / 23x + 75 = 124 / 107

3317x = 2852x + 9300

465x = 9300

x = 20 .

So , the number of women in society after added

= 20 x 23 + 75

= 535 .

So , the number of men in society after added

= 31 x 20

= 620 .

Number of more women is = 620 – 535 = 85 .

**Example 5 :**

In a liquied mixture of 60 litres , the ratio of milk and water is 2 :1 . If this ratio is to be 1 : 2 , then the quantity of water to be further added is :

**Answer :**

So Quantity of milk = ( 60 x 2 / 3 ) = 40 litres.

Water in it = ( 60 – 40 ) = 20 litres .

new ratio required = 1 : 2 .

Let quantity of water to be added further be x liters

milk : water = 40 / ( 20 + x )

Now,

40 / ( 20 + x ) = 1 / 2

20 + x = 80

x = 60 lires

So, 60 litres of water to be added further.

**Example 6 :**

Rs 75,500/- are divided between A and B in the ratio 1 : 3 . what is the difference between thrice the share of A and twice the share of B ?

**Answer :**

Share of A = 75,500 x 1 / 1 + 3 = 75,500 x 1 / 4 = 18875 .

Share of B = 75,500 x 3 / 1 + 3 = 75,500 x 3 /4 = 56625 .

Difference between thrice the share of A and twice the share of B is

= 2B – 3A

= 2 x 56625 – 3 x 18875

= 113250 – 56625

= 56625 .

**Example 7 :**

20% alcohol present in a 15 litres mixture and rest of water . If 3 litres of water be mixed with it , the percentage of alcohol in the new mixture would be ?

**Answer :**

20% present in a 15 litres mixture

So, 20 x 15 / 100 = 3 litres .

Water in it = ( 15 – 3 ) 12 litres .

New quantity of mixture = ( 15 + 3 ) = 18 litres .

Percentage of alcohol in new mix is = ( 3 x 100 / 18 ) % = 50 / 3 .

**Example 8:**

A liquid mixture contain alcohol and water in the ratio of 4 : 3. If 5 liters of water is added to the mixture the ration becomes 4 : 5.Find the quantities of alcohol in the given mixture ?

**Answer :**

Let the quantity of alcohol and water be 4x and 3x liters.

Then,

4x / 3x + 5 = 4 / 5

= 20x = 4(3x + 5)

= 8x = 20

= x = 2.5

Quantity of alcohol = ( 4 x 2.5 ) = 10 liters.