# Quantitative Aptitude – Ratio and Proportion – A solution, of volume 40 litres, has dye and water

## Slot – 1 – Quantitative Aptitude – Ratio and Proportion – A solution, of volume 40 litres, has dye and water

Q. 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?

Solutions:
In the initial 40 liters, we have 16 liters of Dye and 24 liters of water.
To make the ratio as 2:5, we are adding water. Dye will remain 16 liters, so water should become (5/2)*16 = 40 liters
Now we have 16+40 = 56 liters. From this, we will take out 1/4th.
So, we will be left with 42 liters of solution which has Dye and Water in the ratio of 2:5 or 12 liters and 30 liters.
We will add more dye to it so that the ratio becomes 2:3.
Dye is 2/3rd of water = 2/3 of 30 = 20 liters
We need to add 20 – 12 = 8 liters of dye.

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