Question

A container is full of milk, 16 litres of milk is drawn out and replaced with same quantity of water. This process is repeated 2 more times and the ratio of milk and water in the new mixture is 343 : 169. A new mixture is formed by adding 20 litres milk and 30 l in this mixture. Find the ratio of water and  milk in the new mixture.
1. 8 : 7
2. 23 : 66
3. 66 : 23
4. 7 : 8

Answer 1

Correct Answer - Option 2 : 23 : 66

Given:

Ratio of milk and water = 343 : 169

Quantity of milk drawn out = 16 l

Quantity of milk added to form new mixture = 20 l

Concept Used:

When a process is done n times and milk : water = x : y after the process, thenI

In the initial mixture, Milk : Water = (x)^1/n : (y)^1/n

Calculations:

In final mixture,

Ratio of milk and water = 343 : 169

⇒ Ratio of milk, water and total mixture = 343 : 169 : 512

In final mixture, 

Ratio of milk and total mixture = (343)^1/3 : (512)^1/3

⇒ Ratio of milk and total mixture = 7 : 8

Quantity of milk drawn out = 16 l

⇒ (8 – 7) = 1 unit = 16 l

⇒ Quantity of milk = 7 × 16 = 112 l

Quantity of water = (8 – 7) × 16 =  16 l

Now, 20 l milk and 30 l water is added, 

⇒ Quantity of milk in new mixture = (112 + 20) l = 132 l 

⇒ Quantity of water in new mixture = (16 + 30) l = 46 l

Ratio of milk and water in new  mixture = 132 : 46

⇒ Ratio of milk and water in new  mixture = 66 : 23

∴ The ratio of water and  milk in the new mixture is 23 : 66.