A dairyman pays Rs. 6.40 per liter of milk. He adds water

Hi All,

This question can be approached in a couple of different ways, depending on how you 'see' the math involved.

We're told that milk is purchased for Rs 6.40/liter, mixed with some water, then the mixture is resold at Rs 8/liter. We're told that this process leads to a 37.5% profit.

37.5% = 3/8, so we're looking for total revenue that is Rs 6.40 + (3/8)(Rs 6.40)....

1/8 of Rs 6.40 = Rs 0.80, so....
3/8 of Rs 6.40 = Rs 2.40

Thus, that one liter of milk (and whatever water is mixed in) has to generate Rs 6.40 + Rs 2.40 = Rs 8.80 of revenue.

Comparing Rs 8 and Rs 8.80, you'll notice that the second number is exactly 10% greater than the first number. Thus, the amount of water that we need to add must be 10% of the volume of milk. A ratio of water:milk of 1:10 is needed.

Final Answer:

GMAT assassins aren't born, they're made,
Rich
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lets assume he buys 1 ltr of milk at 6.4 rs.

(8.0/6.4) profit % if he was selling 1 ltr of pure milk.

x be the amount of water added to 1 ltr of milk.

(1+x)(8.0/6.4) = 1.375

==> x = 0.1
for 1 ltr 0.1 of water ==>1:10

Let y amount of water be added to 1ltr of water , so {8(1+y)-6.4}/6.4 = 37.5/100
So on solving y=1/10
Hence water to milk ratio is 1/10 so ans is A

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6.4Rs per liter of milk (To make it easier I multiplied with 10) --> 64Rs per liter of milk
8Rs per liter of milk + water (To make it easier I multiplied with 10) --> 80Rs per liter of milk + water

We know that dairyman makes a profi of 3/8 (0.375), M=milk and W=water

64M * 11/8 = 80 * (M+W)
88M = 80M + 80W
8M = 80W
M=10W --> 1:10 ration

I got the correct answer, but is this the correct approach?
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Solution:

We can let x = the amount of water in 1 liter of the mixture and kx = the amount of milk in 1 liter of the mixture (notice that the ratio of water to milk is x : kx = 1 : k and we need to determine the value of k).

Since x + kx = 1, we have:

x(1 + k) = 1

x = 1/(1 + k)

We see that kx = k/(1 + k) liter of milk is in 1 liter of the mixture. Since the profit margin is 37.5% or 3/8 and assuming water incurs no cost, we can create the equation:

8 - k/(1 + k) * 6.4 = k/(1 + k) * 6.4 * 3/8

8 = 6.4k/(1 + k) * 3/8 + 6.4k(1 + k)

8 = 6.4k/(1 + k) * (3/8 + 1)

80 = 64k/(1 + k) * 11/8

640/11 = 64k/(1 + k)

10/11 = k/(1 + k)

We see that k must be 10.

Alternate Solution:

If the dairyman sold 1 liter of (pure) milk at a 37.5% profit, he would sell it for:

6.40 + (6.40)(0.375) = $8.80

But he is adding in some amount of water such that he can still generate 37.5% profit by selling one liter of a water/milk mixture for $8.00.

Since 8.00/8.80 = 80/88 = 10/11, we see that he is selling 10/11 liter of milk and 1/11 liter of water in each liter of milk/water mixture. Thus, the ratio of milk to water is 10 : 1, and the ratio of water to milk is 1 : 10.

Answer: A

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Cost price = Rs 6.4 / litre
Selling price of pure milk = Rs 1.375* 6.4 = Rs 8.8 / litre

Selling price of water + milk = Rs 8 / litre

Ratio of milk : water = 10:1

IMO A
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Let y be volume of milk sold and x volume of milk bought.


8y - 6.4x/6.4x = 37.5/100

8y - 6.4x = 2.4x

8y = 8.8x

y = 1.1x


If volume bought is x, volume of water added would be 0.1x

Water to milk ratio will be

0.1 : 1

1 : 10.

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