Question
A 270-liter solution is composed of Phenyl and water in the
ratio 4:5. After adding 30 liters of Phenyl and (x + 15) liters of water, the ratio becomes 6:7. What is the final ratio of Phenyl to water if an extra ‘5x’ liters of water is added?Solution
ATQ,
Initial quantity of Phenyl = 270 × (4/9) = 120 liters
Initial quantity of water = 270 × (5/9) = 150 liters
According to the question,
(120 + 30):(150 + x + 15) = 6:7
Or, 150 / (x + 165) = 6 / 7
Or, 7 × 150 = 6 × (x + 165)
Or, 1050 = 6x + 990
Or, 6x = 60 → x = 10
So, Phenyl in final mixture = 120 + 30 = 150 liters
Water in final mixture = 150 + 10 + 15 + 5×10 = 150 + 10 + 15 + 50 = 225 liters
Required ratio = 150:225 = 2:3
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