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I02-10 14 Oct 2025, 06:39
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I like the solution - it’s helpful.
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I02-10 19 Oct 2025, 06:58
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I02-10 23 Oct 2025, 08:40
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I02-10 26 Oct 2025, 22:29
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First Mixture - 4:1 - x litres of mixture
Second - 3:2 - y litres of mixture

Lime Concentration / Total Mixture = (x + 2y) / (5x + 5y) = 28/100

x+2y => 28
x+y => 20

x = 12, y = 8

12/20 = 3/5 =>Ratio of first mixture and total mixture volume

Please note that I equated the above equation to form two equations, but since the concentration is a ratio (28%), we only have the values as ratio and x & y MAY be but not necessarily be the actual values.
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I02-10 29 Oct 2025, 14:11
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I02-10 20 Dec 2025, 00:15
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This is a great question that’s helpful for learning.
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I02-10 10 Jan 2026, 04:52
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I don’t quite agree with the solution. If you check whether using 24 liter of the first mixture (20%) and 40 liters of the second mixture (40%) adds up to a 64 liter mixture with 28% lime juice, it doesn't.

24*0.2 + 40*0.4 = x*64
4.8 + 16 = 64x
20.8 = 64x
x = 20.8/64 = 0.325 => which is not 28%

My solution:

0.2*x + 0.4*(1-x) = 0.28
0.2x + 0.4 - 0.4x = 0.28
0.4 - 0.2x = 0.28
0.12 = 0.2x
x = 0.12/0.2 = 12/20 = 3/5 = 0.6 => the whole mixture consists of 3/5 of mixture 1 and 2/5 of mixture 2.

So x:y = 3:2, therefore the solution is 24 liters of mixture 1 and 16 liters of mixture 2.

24*0.2 + 16*0.4 = x*40
4.8 + 6.4 = 40x
x= 11.2/40 = 0.28 => this way the final mixture will be one of 28% lime juice.
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delectussaepe
I don’t quite agree with the solution. If you check whether using 24 liter of the first mixture (20%) and 40 liters of the second mixture (40%) adds up to a 64 liter mixture with 28% lime juice, it doesn't.

24*0.2 + 40*0.4 = x*64
4.8 + 16 = 64x
20.8 = 64x
x = 20.8/64 = 0.325 => which is not 28%

My solution:

0.2*x + 0.4*(1-x) = 0.28
0.2x + 0.4 - 0.4x = 0.28
0.4 - 0.2x = 0.28
0.12 = 0.2x
x = 0.12/0.2 = 12/20 = 3/5 = 0.6 => the whole mixture consists of 3/5 of mixture 1 and 2/5 of mixture 2.

So x:y = 3:2, therefore the solution is 24 liters of mixture 1 and 16 liters of mixture 2.

24*0.2 + 16*0.4 = x*40
4.8 + 6.4 = 40x
x= 11.2/40 = 0.28 => this way the final mixture will be one of 28% lime juice.
Show more

Please read the question carefully. Your check is using 40 liters as the second mixture, but the table’s 40 is the final mixture, not the second mixture.



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I02-10 28 Jan 2026, 12:30
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I did not quite understand the solution. Did not understand the last 2 lines
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I did not quite understand the solution. Did not understand the last 2 lines
Show more

From 0.2x + 0.4y = 0.28(x + y), we simplify to 2x = 3y, so y = 2x/3.

Then the final mixture amount is x + y = x + 2x/3 = 5x/3.

So the ratio (first mixture):(final mixture) is x/(5x/3) = 3/5.

That means the two selected numbers must be in a 3:5 ratio. Among the choices, only 24 and 40 fit since 40 = (5/3)·24.

Hope it's clear.
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I02-10 10 Feb 2026, 18:38
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I did not quite understand the solution. i dont understand the part where the ration explanation starts
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