CAT 2020 Ratio, Proportion and Variation Question (Hard)

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?

Accepted Answer

Step 1 Initial solution Volume 40 litres Dye Water 2 3 Total parts 5 - Dye 2 5 40 16 litres - Water 3 5 40 24 litres Step 2 Add water to make ratio 2 5 Let x litres of water be added New water 24 x Dye remains 16 litres Now Dye Water 2 5 16 24 x 2 5 Cross-multiplied 5 16 2 24 x 80 48 2x 2x 32 x 16 l

CAT 2020

Quantitative

Ratio, Proportion and Variation

Hard

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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