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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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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

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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qlx
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

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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Consider zero adultration

Now the selling price for 1L milk = 6.4 * 1.375 = 8.8

So, for every 8 rs. of milk sold o.8 is water i.e. 10%

If not understood form the equation 8(M + W) = 8.8 M

8W = 0.8M

W/M = 1/10
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