Let’s see the table below, write in mathematical language and try to find out the answer.

For easy way let assume given mixture is of milk and water

1. ratio of milk and water in first type of mixture = 5:4

ratio of milk and water in second type of mixture = 3:2

milk in first type of mixture

Water in first type mixture

Milk in second type of mixture

Water in second type of mixture

Given that equal quantities are taken from two mixture. Let x unit is taken from both mixtures.

So, milk in new type of mixture =

And, water in new mixture =

Hence,

Ratio of milk to water in new mixture

Milk: water = 26:19

2. For easy way let assume given mixture is of milk and water

ratio of milk and water in first type of mixture = 4:5

ratio of milk and water in second type of mixture = 5:1

ratio of milk and water in new mixture = 5:4

Suppose kg of first type and y kg of second type taken and mixed

Quantity of milk in in new mixture

Total quantity of new mixture = ( )

Hence,

8 + 15y = 10 + 10y

⇒ 2 = 5y

⇒ x: y = 5:2

3. ratio of milk and water in first type of mixture = 3:4

ratio of milk and water in second type of mixture = 9:5

For easy way let assume given mixture is of milk and water

milk in first type of mixture

Water in first type mixture

Milk in second type of mixture

Water in second type of mixture

Given that, the ratio of the quantities of two mixtures in the new mixture is 1:2

So, milk in new type of mixture

And, water in new mixture

Hence,

Ratio of milk to water in new mixture

Milk: water = 4:3

4. For easy way let assume given mixture is of milk and water

ratio of milk and water in first type of mixture = 2:3

ratio of milk and water in second type of mixture = 5:4

ratio of milk and water in new mixture = 1:1

Suppose x kg of first type and y kg of second type taken and mixed

Quantity of milk in in new mixture

Total quantity of new mixture = ( )

Hence,

⇒ 9= 5y

⇒ : y = 5:9

5. For easy way let assume given mixture is of milk and water

ratio of milk and water in first type of mixture = 4:3

ratio of milk and water in second type of mixture = 5:2

ratio of milk and water in new mixture = 9:5

Suppose kg of first type and y kg of second type taken and mixed

Quantity of milk in in new mixture

Total quantity of new mixture = ( )

Hence,

⇒ 8+ 10y = 9 + 9y

⇒ = y

⇒ : y = 1: 1