# CAT 2020 Question Paper | Quants Slot 1

###### CAT Previous Year Paper | CAT Quants Questions | Question 26

This question is from Mixture and Alligation. This question talks about a solution that consists of dye and water in a specified proportion. We need to find the quantity of dye that is needed to be added to achieve the initial proportion of dye and water after some alteration. The importance of Arithmetic questions has increased significantly in the CAT exam. The Arithmetic section plays a pivotal role in your CAT Preparation. Make sure you master this topic by practicing a lot of questions from the 2IIM CAT Question Bank.

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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