Question: A dairyman pays Rs. 6.40 per liter of milk. He adds water and sells the mixture at Rs. 8per liter, thereby making 37.5% profit. The proportion of water to milk received by the customers is

(a) 1:10
(b) 1:12
(c) 1:15
(d) 1:20
(e) 1:25

Correct Answer: (A)
Solutions and Explanation
Approach Solution - 1 :

It is given that with a profit of 37.5% (or 3/8) of the cost price, the selling price is Rs 8 per litre.
Therefore, Price at Cost*(1 + 3/8) = 8
Price Cost = 64/11

As a result, he only uses up milk worth Rs. 64/11 for each liter he sells.
1 liter of milk is available for Rs 6.4.
For Rs. 64/11, the liters of milk received is, 64/(11*6.4) = 10/11 liters of milk
He must be adding 1/11 liters of water to it because he only uses 10/11 liters of milk.

Therefore, the ratio of water to milk is 1:10.

Approach Solution - 2 :

The equation can be written as the following assuming that the ratio of milk to water is x:1.
Selling price of (1 liter Milk + x liters of Water) - 1 liter Milk's cost = 1 liter milk's profit.

[Note that 37.5% = 3/8]
=> 8(1+x) − 6.4 = 6.4(3/8)
=> 8x − 1.6 = 2.4
=> x = 1/10

The ratio therefore is 1:10.

Approach Solution - 3 :

If only milk were sold at Rs 8 per liter, the dairyman would make a 25% profit.
Milk and water sales generate a profit of 37.5%, so selling only water generates an additional 12.5% profit.
80 paise is the 12.5% of Rs. 6.40. This can be used to purchase one-tenth of a liter of milk from Dairyman.
Because of this, customers receive a 1:10 milk to water ratio.

“A dairyman pays Rs. 6.40 per liter of milk. He adds water” - is a subject that the GMAT quantitative reasoning section covers. A school needs to be proficient in a variety of qualitative skills to answer the GMAT Problem Solving questions correctly. There are 31 questions in the GMAT Quant section as a whole. The GMAT Quant topics' problem-solving section calls for the resolution of calculative mathematical puzzles.

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