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?

Answer 1

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

Quantity of water added = $16$ $litres$ (As $1$ part = $8$ $litres$).

Quantity of dye and water removed = $\frac{1}{4}×\frac{2}{7}(56)$ i.e., $4$ litres and $\frac{1}{4}×\frac{5}{7}×(56)$ i.e., $10$l litres.

Final quantity of dye and water is $12$ litres and $30$ litres.

$∴$ Quantity of dye to be added to make the ratio of dye and water again $2: 3$ i.e., $8$ litres.