10 litres are removed from 80 litres of solution of milk and water having ratio of milk and water as 4 : 3 and replaced with water. This operation is done a total of three times. What is the ratio of milk and water in the solution now ?


A. 47/128
B. 48/128
C. 49/128
D. 50/128
E. 51/128
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TWIN QUESTION: https://gmatclub.com/forum/10-litres-ar ... 14165.html
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Can somebody please solve this ? I am not able to crack this question. Thanks.

I have checked and rechecked but I am getting 49/79 as the ratio of Milk:Water in the resultant solution.

Initial qty of milk in the 80 L solution is (80/7)*4=320/7. Qty of milk remaining after 10 L of solution is removed and replaced with 10 L of water three times is (320/7)*(7/8)^3=(5*49)/8. Since the qty of solution remains unchanged, the qty of water becomes 80-(5*49)/8. Therefore, the ratio of Milk to Water in the final solution is 49/79. IMO, had the question asked for the FRACTION of Milk in the final solution then the answer would be 49/(79+49)=49/128.

Final qty of milk =
4/7×(1-10/80)^3
= 49/128
Final ratio of milk and water
= 49/79
Final qty=
initial qty(1- qty repl/tot qty)^number of times repl

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Hi,

Can someone please confirm this.
The question asks for ratio of milk to water which is 49:79
ratio of milk to solution = 49:128
(this is also confirmed in the twin question as mentioned by Bunnel above which asks quantity of milk in final solution = 49/128 * 80 = 245/8 L)
ratio of water to solution = 79 : 128

Similar question:
https://gmatclub.com/forum/12-5-of-a-so ... 89617.html

Hi Bunuel,

I am getting ratio of milk and water as 49: 79. Could you please check the options.

Regards,
Abhee

There is an error in the options. The denominator has to be 79 and not 128 (which is the denominator if you're comparing the ratio of milk to new solution).

Yeah i think the question is phrased incorrectly.
The solutions are for the final result of water in the mixture (49/128), not for the ratio of milk to water.

4/7*(1-10/80)^3
4/7(70/80)^3
4*7*(7/8)^3
1/2*7/8*7/8 = 49/128

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