Average, Mixture and Alligation Question 3 - CAT 2020
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-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 : 3?
Step-by-Step Explanation
- Analyze the Initial State:
Initial volume = 40 litres. Ratio of dye to water is 2 : 3.
Dye = 2 / 5 × 40 = 16 litres, Water = 3 / 5 × 40 = 24 litres
- Analyze the Dilution State:
Water is added to change the proportion to 2 : 5. Because no dye was added, the absolute quantity of dye remains exactly 16 litres.
16 / New Water = 2 / 5 ⟹ New Water = 40 litres
- Analyze the Removal Step:
One-fourth (1 / 4) of this diluted mixture is discarded, which means 3 / 4 of each individual component remains:
Remaining Dye = 16 × 3 / 4 = 12 litres
Remaining Water = 40 × 3 / 4 = 30 litres
- Calculate the Final Target:
We want to bring the final concentration back to the original 2 : 3 ratio by adding dye. The water volume stays locked at 30 litres.
Target Dye / 30 = 2 / 3 ⟹ Target Dye = 20 litres
Dye to be added = 20 − 12 = 8 litres
Correct Answer: 8
💡 FundaMakers Tip:
Ignore total mixture volumes when removing fractions of a solution. When you discard 1 / 4 of a blended container, every component drops by exactly 25%. Scaling the individual component weights down directly by 3 / 4 simplifies your scratchpad bookkeeping and avoids calculation errors.