Question

the ratio of water and milk into different containers is 2:3 and 4:5 find the ratio in which one is required to mix the mixture of two continents so that one gets the new mixture of milk and water in the ratio of 7:5​

Answer 1

Consideration :

Let, the two mixtures will be mixed into the ratio x : y

First mixture :

Water : Milk = 2 : 3

Water = 2/5 & Milk = 3/5

In x amount of first mixture,

• Water = 2x/5
• Milk = 3x/5

Second mixture :

Water : Milk = 4 : 5

Water = 4/9 & Milk = 5/9

In y amount of second mixture,

• Water = 4y/9
• Milk = 5y/9

Mixed mixtures :

If two containers of mixtures will be mixed,

• Water = 2x/5 + 4y/9 = (18x + 20y)/45
• Milk = 3x/5 + 5y/9 = (27x + 25y)/45

Given :

In new mixture, Milk : Water = 7 : 5

⇒ (27x + 25y)/45 : (18x + 20y)/45 = 7 : 5

⇒ (27x + 25y)/(18x + 20y) = 7 : 5

⇒ 5 (27x + 25y) = 7 (18x + 20y)

⇒ 135x + 125y = 126x + 140y

⇒ 135x - 126x = 140y - 125y

⇒ 9x = 15y

⇒ x/y = 15/9 = 5/3

⇒ x : y = 5 : 3

∴ the required ratio of two mixtures be 5 : 3