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Dye added to solution

CAT 2020 Slot 1 · Quantitative Ability · Medium · Ratio and Proportion

This is a medium Quantitative Ability question from the CAT 2020 Slot 1 paper. It tests Ratio and Proportion. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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A solution, of volume 40 litres, has dye and water in the proportion 2:32 : 3. Water is added to the solution to change this proportion to 2:52 : 5. If one-fourth 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 2:32 : 3?

(TITA)

Answer

8

Explanation

  1. Initial Solution (40 L, Dye : Water = 2 : 3): Dye=25×40=16 L,Water=24 L\text{Dye} = \frac{2}{5} \times 40 = 16\text{ L}, \quad \text{Water} = 24\text{ L}

  2. Water added to make proportion 2 : 5: Dye remains 16 L. New Water=16×52=40 L\text{New Water} = 16 \times \frac{5}{2} = 40\text{ L} Total diluted volume =16+40=56 L= 16 + 40 = 56\text{ L}.

  3. One-fourth taken out: Remaining volume is 34\frac{3}{4} of the diluted solution: Remaining Dye=16×34=12 L\text{Remaining Dye} = 16 \times \frac{3}{4} = 12\text{ L} Remaining Water=40×34=30 L\text{Remaining Water} = 40 \times \frac{3}{4} = 30\text{ L}

  4. Add dye to bring proportion back to 2 : 3: Let dd litres of dye be added. 12+d30=23  ⟹  12+d=20  ⟹  d=8 litres\frac{12 + d}{30} = \frac{2}{3} \implies 12 + d = 20 \implies d = 8\text{ litres}

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