A Milkman Sells Milk after Adding Some Water in it GMAT Problem Solving

Question: A milkman sells milk after adding some water in it. Quantity of water is 74% of quantity of milk in mixture. If milkman sells the mixture (milk + water) at 16.66% discount (16.66% less price than CP of pure milk) find the profit %of milkman?

1. 37%
2. 40%
3. 45%
4. 50%
5. 57.5%

“A milkman sells milk after adding some water in it. Quantity of water is 74% of quantity of milk in mixture. If milkman sells the mixture (milk + water) at 16.66% discount (16.66% less price than CP of pure milk) find the profit %of milkman?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Answer:

Approach Solution 1:

Le the milk is 100 litres
Water added 74% = 100 * 0.74 = 74 litre
Total mixture = 174 litre
Let rate per lire is $1
Discounted price for 174 litre of milk mixture = 174 * (1 – 0.1666) = 145
Profit % = 45%

Correct option: C

Approach Solution (2):

Since the answer options are in percentage, we can take numbers and work to get out the answer
Let us assume the milkman bough 100 liters of milk in $100 (His cost price)
Now we know the quantity of water is 74% of the quantity of milk in the mixture. This means that in these 100 liters of milk, he added \(\frac{74}{100}\) times 100 = 74 liters of water
So the total mixture = 100 + 74 = 174 litres
Now ideally he should sell this 174 liters mixture in $174 but he gives a 16.66% discount.
So, the selling price = SP = 174 - \(\frac{16.66}{100}*174\)= 174 - \(\frac{1}{6}*174\)= 174 – 29 = 145
Thus the milkman bought the milk for $100 and sold it for $145
Hence profit = 145 – 100 = 45
Profit percent = \(\frac{45}{100}*100\) = 45%

Correct option: C

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