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A container is filled with 56 litres of pineapple juice. 8 litres of

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Bunuel
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A container is filled with 56 litres of pineapple juice. 8 litres of [#permalink] New post   21 Jan 2021, 22:22
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A container is filled with 56 litres of pineapple juice. 8 litres of pineapple juice are extracted and the container is refilled with mango juice. The content of the container is thoroughly mixed and 8 litres of the mixture are then extracted and the container is again refilled with mango juice. What is the ratio of mango juice to pineapple juice in the final mixture?

A. 13:36
B. 2:5
C. 27:62
D. 36:13
E. 6:1

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Re: A container is filled with 56 litres of pineapple juice. 8 litres of [#permalink] New post   21 Jan 2021, 23:28
First there was 56 litres of pineapple juice.
After extracting 8 litres of pineapple juice and refilling with mango juice, there will be 8 litres of mango juice and 48 litres of pineapple juice.
If we extract 8 litres from the mixture and refill with mango juice, then there will be 8-(8/56)*8+8=107/7 litres of mango juice and 48-(48/56)*8=288/7 litres of pineapple juice in the mixture. The ratio of mango juice to pineapple juice=(107/7):(288/7)=107:288=13:36 A)
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Re: A container is filled with 56 litres of pineapple juice. 8 litres of [#permalink] New post   22 Jan 2021, 00:32
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ratio after 1st operation.
P: M
48:8
6:1

Ratio after 2nd ops.
Pineapple :: 48-6/7*8 (as 8lts is taken out)
Mango :: 8-1/7*8 + 8 (as 8lts is taken out & then 8lts of mango is again getting added)

M:P = (8-1/7*8 + 8) : (48-6/7*8)
M:P = 13:36
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Re: A container is filled with 56 litres of pineapple juice. 8 litres of [#permalink] New post   22 Jan 2021, 02:01
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Bunuel wrote:
A container is filled with 56 litres of pineapple juice. 8 litres of pineapple juice are extracted and the container is refilled with mango juice. The content of the container is thoroughly mixed and 8 litres of the mixture are then extracted and the container is again refilled with mango juice. What is the ratio of mango juice to pineapple juice in the final mixture?

A. 13:36
B. 2:5
C. 27:62
D. 36:13
E. 6:1

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Check this post on replacement first: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2012/0 ... -mixtures/

Replacement takes place twice. We work with pineapple juice because it is not added back.

Cf = Ci * (Vi/Vf)^2

Cf = 1 * (48/56)^2

Cf = 36/49

The final concentration of pineapple juice in the mixture is 36/49. This means we have 36 parts of pineapple juice and 13 parts of mango juice in 49 parts of total mixture.

Answer (A)
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Re: A container is filled with 56 litres of pineapple juice. 8 litres of [#permalink] New post   06 Dec 2022, 15:23
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