Problem Solving

A bucket contains 1 litre of milk. A milkman removes 10% of the content of the bucket and replaces it with water. The next day the milkman again does the same operation and removes 10% of the contents of the bucket and replaces it with water. He then sells the one litre of milk to a customer at the rate of $12 per litre. If the milkman had purchased the milk at $10 per litre what is his profit percentage on his cost price keeping in mind that due to his mixing he was able to save some additional milk?

(A)20%
(B) 48.15%
(C) 50%
(D)55.45%

sgr21 wrote:A bucket contains 1 litre of milk. A milkman removes 10% of the content of the bucket and replaces it with water. The next day the milkman again does the same operation and removes 10% of the contents of the bucket and replaces it with water. He then sells the one litre of milk to a customer at the rate of $12 per litre. If the milkman had purchased the milk at $10 per litre what is his profit percentage on his cost price keeping in mind that due to his mixing he was able to save some additional milk?

(A)20%
(B) 48.15%
(C) 50%
(D)55.45%

To make the math easier, let the bucket = 100 liters.

After 10% is removed, the amount of milk remaining in the bucket = 100 - (10% of 100) = 90 liters.
After another 10% is removed, the amount of milk remaining in the bucket = 90 - (10% of 90) = 81 liters.

At a cost price of $10 per liter, the total cost for the 81 liters of milk in the bucket = 10*81 = $810.
At a selling price of $12 per liter, the selling price for the entire 100-liter bucket = 12*100 = $1200.
Profit = 1200-810 = $390.

Profit percentage = profit/cost * 100 = 390/810 * 100 = 13/27 * 100 = (less than 1/2) * 100 = a bit less than 50%.

The correct answer is B.

This looks like a question from the Indian CAT - totally fair game, I think.

Here would be my approach:

The milkman pays $10 per liter.

He replaces 10% of the milk, leaving us with 900ml of milk and 100ml of water. He then replaces another 10% of the milk, leaving us with 810ml of milk and 190ml of water.

He then sells 810ml, or .81 liters, for $12. To figure out how much he earned per liter, just set up a ratio:

.81 1.00
--- = ----
$12 $x

.81x = 12
81x = 1200
x = 14.8148148... = ~$14.81

He paid $10, he makes $14.81, so he enjoys an ~48% profit. Nice question!

By the way, a cool trick for the division:

81x = 1200
x = 1200/81 = 400/27

27 * 37 = 999, and we know anything over 999 repeats as follows (xyz/999) = .xyzxyzxyz...

So if x = 400/27, it's also (400*37)/(27*37), or (14800)/999, or 100 * 148/999 = 100 * .148148148148...

That was too neat not to pass along