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Bunuel
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Mayukhca2018
The language is very confusing:

"Sugar by water" means
Sugar/Water = 20%.

If you go ahead a solve it. It doesn't match the options

But if you consider "Sugar by Water" as Sugar/(Sugar + Water)= 20% and voila we have our answer as E. 2 litres.

Posted from my mobile device


Wouldn't sugar + water always be a 100%.

Ratio of Sugar /water = 20/80
Ratio of Sugar/Sugar +water = 20/100

I could not understand what has changed?
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Bunuel
A sugar syrup (solution of sugar in water) contains 20% sugar by water. How much water must be added to 8 litres of syrup for the content of sugar in the solution to be made 16% ?

(A) 8 litres
(B) 6 litres
(C) 5 litres
(D) 4 litres
(E) 2 litres

WATER SUGAR SYRUP
0% (SUGAR) 20% (SUGAR)

16%(SUGAR)

4% 16%

That is 1:4
We have 8 Ltr of Syrup
So we need 2 ltr of water.

Please, correct if wrong.

Thanks
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mohammadfaraaz123
Mayukhca2018
The language is very confusing:

"Sugar by water" means
Sugar/Water = 20%.

If you go ahead a solve it. It doesn't match the options

But if you consider "Sugar by Water" as Sugar/(Sugar + Water)= 20% and voila we have our answer as E. 2 litres.

Posted from my mobile device


Wouldn't sugar + water always be a 100%.

Ratio of Sugar /water = 20/80




I could not understand what has changed?

1. Since its ratio (Sugar by water) Sugar/water = 20/100(since 20% can be represented as 20/100). That means total sugar syrup = 100+20=120.

The above interpretation if we solve, we get very different answer(answer will be 25/3-8=0.33 litres)

2. If solve by reading Sugar by water as Sugar/Sugar Syrup = 20/100. Then the solution will be different.

Thats why I caveated that the language is confusing and ambigious.

If we consider the second understanding then it gives an answer as 2 Litres.
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The key thing to note here would be that the amount of sugar remains unchanged; only the water content changes.

Approach 1:
We could take an algebraic approach.
Initial amount of sugar=(20/100)*8 .....[1]
Let 'V' litres of water be added.
Final amount of sugar=(16/100)*(V+8)...[2]
[1]=[2] and solving for V would give us V=2 litres.

Approach 2:
Initial percentage of sugar is 20% and this is 20% of 8 litres and so the amount of sugar is 1.6
Now since amount of sugar remains unchanged, this 1.6 is now 16% of a new total volume.
16% is 1.6, 4% would be 0.4 and 100% would be 25*0.4=10 litres.So the volume of water added would be 2 litres.

Hope this helps!
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Isa1989
The key thing to note here would be that the amount of sugar remains unchanged; only the water content changes.

Approach 1:
We could take an algebraic approach.
Initial amount of sugar=(20/100)*8 .....[1]
Let 'V' litres of water be added.
Final amount of sugar=(16/100)*(V+8)...[2]
[1]=[2] and solving for V would give us V=2 litres.

Approach 2:
Initial percentage of sugar is 20% and this is 20% of 8 litres and so the amount of sugar is 1.6
Now since amount of sugar remains unchanged, this 1.6 is now 16% of a new total volume.
16% is 1.6, 4% would be 0.4 and 100% would be 25*0.4=10 litres.So the volume of water added would be 2 litres.

Hope this helps!

Hi Isa,
In both approaches the basic assumption is that 20% is content of sugar in Sugar Syrup.
However the question says 20% is sugar by water(which translates to Sugar/Water = 20%, which as per me is different from Sugar/Sugar Syrup). Am I missing something here.

Posted from my mobile device
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Mayukhca2018
Isa1989
The key thing to note here would be that the amount of sugar remains unchanged; only the water content changes.

Approach 1:
We could take an algebraic approach.
Initial amount of sugar=(20/100)*8 .....[1]
Let 'V' litres of water be added.
Final amount of sugar=(16/100)*(V+8)...[2]
[1]=[2] and solving for V would give us V=2 litres.

Approach 2:
Initial percentage of sugar is 20% and this is 20% of 8 litres and so the amount of sugar is 1.6
Now since amount of sugar remains unchanged, this 1.6 is now 16% of a new total volume.
16% is 1.6, 4% would be 0.4 and 100% would be 25*0.4=10 litres.So the volume of water added would be 2 litres.

Hope this helps!

Hi Isa,
In both approaches the basic assumption is that 20% is content of sugar in Sugar Syrup.
However the question says 20% is sugar by water(which translates to Sugar/Water = 20%, which as per me is different from Sugar/Sugar Syrup). Am I missing something here.

Posted from my mobile device

Hi Mayukh,
I understand the confusion.Generally, I have mostly encountered solute percentages as part of the solution(sugar+water) and not just the solvent(water) which is what I went with actually while attempting the question.The language could have been clearer I guess.
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0.2*8 = 1.6L sugar
\(\frac{1.6L sugar}{10 L water}\) = 16% sugar
10-8=2L water added
Ans=E
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Deconstructing the Question

Initial syrup = 8 litres at 20% sugar.

Amount of sugar stays constant when water is added.

Initial sugar:

\(0.20 \times 8 = 1.6\)

Let x be the litres of water added.

Final volume:

\(8 + x\)

Final concentration is 16%:

\(\frac{1.6}{8+x} = 0.16\)

Step-by-step

\(1.6 = 0.16(8+x)\)

\(1.6 = 1.28 + 0.16x\)

\(0.32 = 0.16x\)

\(x = \frac{0.32}{0.16} = 2\)

Answer: E
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