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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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