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?
Explanation:
40 litres solution had dye and water in the ratio 2 : 3
∴ dye = 16 l and water = 24 l.
After adding x liters of water, now proportion is 2 : 5
⇒ 1624+x=25
⇒ x = 16 liters
Dye = 16 l and water = 40 l now in the solution.
Now, 1/4th is removed from the solution, hence dye left = ¾ × 16 = 12 l and water left = ¾ × 40 = 30 l
Now, After adding y liters of dye, proportion becomes 2 : 3.
⇒ 12+y30=23
⇒ y = 8 liters
Hence, 8.
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