CAT 2020 Quant Question [Slot 1] with Solution 24

Question

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?

Option: 8
Solution:

Original quantity of dye and water in the original solution i.e., 16 litres (i.e. \(\left. { = 40 \times \frac{2}{5}} \right)\) and 24 litres (i.e. = \(40 - 16)\)

Quantity of water added \( = 16\) litres (As 1 part \( = 8\) litres). Quantity of dye and water removed \( = \frac{1}{4} \times \frac{2}{7}(56)\) i.e., 4 litres and \(\frac{1}{4} \times \frac{5}{7} \times (56)\) i.e., 10 litres. Final quantity of dye and water is 12 litres and 30 litres.

\(\therefore \) Quantity of dye to be added to make the ratio of dye and water again 2: 3 i.e., 8 litres.

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CAT 2020 Quant questions with Solutions