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120 litre orange juice was mixed with 20 litre water. 7 litre of this mixture was taken out and 'X' litre of water was added and therefore the resultant ratio between orange juice and water in the mixture was 19:4 respectively. If 23 l mixture was again taken out, what was the resultant quantity of water in the final mixture?

Given ans: 24 l ....My answer 20 l. Where may have I gone wrong?

My Soln:

Orange juice=120l(given)

Water =20l (Given)

Ratio=6:1

Quantity of mixture taken out=7l(Given)

Amount of orange jouice taken out=(6/7)*7=6l

Amount of water taken out=(1/7)*7=1l

Resultant Orange juice=120-6=114l

Resultant Water=20-1+X=(19+X)l

114/(19+X)=19/4

X=5l

Resultant Orange juice=114l

Resultant Water=19+5=24l

Ratio=19:4

Quantity of mixture taken out again = 23l(Given)

Water taken out=(4/(19+4))*23=4l

Remaining water=24-4=20l.

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    Allegation? Did you mean something else? – 2017-01-15
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    Yes I meant alligation. We do problems based on mixtures and term it alligation. – 2017-01-15
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    @KanwaljitSingh I rolled back your title edit since the OP really meant [alligation](https://en.wikipedia.org/wiki/Alligation), *not* allegation. – 2017-01-15
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    @dxiv I think user has spelling mistake that's why I edited that. – 2017-01-15
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    i got x was 9.84L but im not sure im reading it right. perhaps post the original question how it was worded – 2017-01-15

1 Answers 1

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Your solution is correct.

When first time mixture taken out then quantity of water left 19 l.

After that on adding some amount of water. On solving we get that amount is 5 l.

Amount of water is now 24 l.

After that on again taking out 23 l of mixture 4 l water is taken out.

Final amount of water 20 l. That is the answer if asked about final quantity of water.

As you said answer is 24 l. Maybe answer given in book is wrong. Or they are asking about amount of water after adding 5 l ( that you found) water in solution.

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    @Faust I hope now its easy to read for you. – 2017-01-15
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    Sorry i didn't mean your post i put that in the wrong place :( very sorry. i meant the original post i agree with your solution – 2017-01-15
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    @Faust its ok. No need to say sorry. – 2017-01-15
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    @Faust if you have any problem in understanding question. Can I help you? Please tell me. – 2017-01-15