A dishonest milkman sells milk to three customers- A, B and C. He replaces 20% of pure milk with water before selling to A. After this, he replaces 25% of the mixture with water before selling to B and furthermore 30% of the mixture is replaced before selling to C. What is the percentage of pure milk in the mixture sold by the milkman to C?a)44%b)38%c)35%d)42%Correct answer is option 'D'. Can you explain this answer?

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A dishonest milkman sells milk to three customers- A, B and C. He replaces 20% of pure milk with water before selling to A. After this, he replaces 25% of the mixture with water before selling to B and furthermore 30% of the mixture is replaced before selling to C. What is the percentage of pure milk in the mixture sold by the milkman to C?

a)
44%
b)
38%
c)
35%
d)
42%

Correct answer is option 'D'. Can you explain this answer?

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A dishonest milkman sells milk to three customers- A, B and C. He repl...

Since, the milk is getting replaced by water, we will use the formula M' =

where M, r1, r2 and r3 are the milk's proportion in the beginning, % of milk replaced before selling to A, % of milk replaced before selling to B and % of milk sold before selling to C, respectively.

Milk % before selling to C = M' =

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A dishonest milkman sells milk to three customers- A, B and C. He repl...

To solve this problem, we need to understand the process of each sale and calculate the percentage of pure milk after each replacement. Let's break it down step by step:

Step 1: Replacement before selling to A
The milkman replaces 20% of pure milk with water. So, if we assume the initial quantity of milk to be 100 units, he replaces 20 units with water, leaving us with 80 units of pure milk.

Step 2: Replacement before selling to B
Now, the milkman takes the 80 units of milk (after the replacement in step 1) and replaces 25% of it with water.
25% of 80 units = 0.25 * 80 = 20 units
So, he replaces 20 units of milk with water, leaving us with 60 units of pure milk.

Step 3: Replacement before selling to C
Finally, the milkman takes the 60 units of milk (after the replacement in step 2) and replaces 30% of it with water.
30% of 60 units = 0.30 * 60 = 18 units
So, he replaces 18 units of milk with water, leaving us with 42 units of pure milk.

Therefore, the percentage of pure milk in the mixture sold by the milkman to C is:
(42 units / 100 units) * 100% = 42%

Hence, the correct answer is option D) 42%.

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