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There is a 40 litre solution of milk and water with concentration of milk as 30%. 10 litres of the solution is replaced with 10 litres of water. After some time, 10 litres of the new solution is replaced with 10 litres of milk. What is the concentration of milk in the solution now?

There is a 40 litre solution of milk and water with concentration of milk as 30%. 10 litres of the solution is replaced with 10 litres of water. After some time, 10 litres of the new solution is replaced with 10 litres of milk. What is the concentration of milk in the solution now? Correct Answer 41.875%

From the data given in the problem, we can conclude the solution from the table below

 

Milk

Water

Total

Initial

(30% of 40) = 12

(40 - 12) = 28

12 + 28 = 40

After taking out 10 litres of solution

(In the ratio 12 ∶ 28 = 3 ∶ 7)

× 10 = 3

12 - 3 = 9

× 10 = 7

28 - 7 = 21

9 + 21 = 30

After adding 10 litres of water

9

21 + 10 = 31

9 + 31 = 40

Take out 10 litres of solution

(In the ratio 9 ∶ 31)

× 10 = 2.25

9 - 2.25 = 6.75

× 10 = 7.75

31 - 7.75 = 23.25

6.75 + 32.25 = 30

Add 10 litres of Milk

10 + 6.75 = 16.75

23.25

16.75 + 23.25 = 40

 

⇒ Required concentration = (16.75/40) × 100%

⇒ 41.875%

∴ Required concentration = 41.875%

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