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Question 26 : A solution, of volume 40 litres, has dye and water in the proportion 2 : 3. Water is added to the solution to change this proportion to 2 : 5. If one-fourths of this diluted solution is taken out, how many litres of dye must be added to the remaining solution to bring the proportion back to 2 : 3?

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Explanatory Answer

40 litres is split in ratio 2:3
So dye = 16 l and water = 24 l
Now proportion is 2:5
Already in the ratios 2:3
2 : 5
Now, 16 l of dye : 40 l of water
16 l of water is added
\\frac{1}{4})th is removed from the proportion
12 l of dye : 30 l of water
Now how many dye has to be added to make 2 : 3
2 : 3
12 l of dye : 30 l of water
Multiplication factor is 10 (3 × 10 = 30)
2 × 10 = 20 l of dye in total,
So 8 l of dye has to be added

The answer is, " 8"

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