The diluted Milk contains only 8 liters of Milk and the rest is water. A new mixture whose concentration is 30%, is to be formed by replacing Milk. How many liters of the mixture shall be replaced with pure Milk if there was initially 32 liters of water in the mixture?a)3 litreb)4 litrec)8 litred)5 litree)None of theseCorrect answer is option 'D'. Can you explain this answer?

Question

Answer

Answer – D. 5 litre Explanation : Milk : Water 8 : 32 => 1:4
Original Ratio = 20%:80% Required Ratio = 30%:70% Original Ratio(water) = 80% Required Ratio(water) = 70% 7/8 = (1-x/40) x = 5 litre

Answer

Given:
- Diluted milk contains only 8 liters of milk and the rest is water.
- A new mixture whose concentration is 30% is to be formed by replacing milk.
- Initially, there were 32 liters of water in the mixture.

To find: How many liters of the mixture shall be replaced with pure milk.

Solution:

Let's assume that we need to replace x liters of the mixture with pure milk.

Since the concentration of the new mixture is 30%, we know that 70% of the mixture is water.

Initial amount of water in the mixture = 32 liters

Final amount of water in the mixture (after replacing x liters of the mixture with pure milk) = 0.7(8 + x)

Final amount of milk in the mixture (after replacing x liters of the mixture with pure milk) = 0.3(8 + x)

We know that the new mixture is formed by replacing x liters of the mixture with pure milk.

So, we can say that:

- Amount of milk in the new mixture = Amount of milk in the original mixture + x

- Amount of water in the new mixture = Amount of water in the original mixture - x

We can now write an equation based on the above information:

0.3(8 + x) = (8 + x)/(8 + x + 32 - x)

Simplifying the equation, we get:

0.3(8 + x) = (8 + x)/40

12 + 0.3x = 0.2x + 2.4

0.1x = 9.6

x = 96/10 = 9.6

Therefore, we need to replace 9.6 liters of the mixture with pure milk to get a new mixture with a concentration of 30%.

Since we can't replace 0.6 liters of the mixture, we need to round off the answer to the nearest whole number, which is 10.

Hence, the answer is option D, 5 liters.

Answer

Given :-
Milk = 8 L ;
Water = 32 L ;

Ratio of Milk to Water = 8 : 32 = 1: 4 ;

i.e., 20 % of milk & 80 % of water ( ORIGINAL RATIO ) ;

New mixture concentration is 30 % ;

i.e., 30 % of milk & 70 % of water ( REQUIRED RATIO ) ;

REQUIRED RATIO/ORIGINAL RATIO = 1- ( X/40 ) ;

Here , 40 is the Total Quantity ( Varies from sum to sum ) ;

70/80 = 1- ( X/40) ;

7/8 = ( 40 - X ) / 40 ;

35 = 40 - X ;

X = 40 - 35 = 5 L ;

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