Question
Download Solution PDFA container contains two liquids, X and Y, in the ratio 5 ∶ 3. When 8 liters of the mixture is drawn off, and the container is filled with liquid Y, the ratio of X to Y becomes 2 ∶ 3. How many liters of liquid X was in the container initially?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Initial ratio of two liquids X and Y = 5 ∶ 3
Mixture drawn = 8 liters
New ratio of X and Y = 2 ∶ 3
Formula Used:
Let the initial quantity of liquid X be 5x and liquid Y be 3x.
Total quantity of mixture = 5x + 3x
Liquid X in 8 liters mixture = \(\frac{5x}{5x + 3x}\) × 8
Liquid Y in 8 liters mixture = 8 - Liquid X in 8 liters mixture
Calculation:
Let the initial quantity of liquid X be 5x and liquid Y be 3x.
Total quantity of mixture = 5x + 3x = 8x
Liquid X in 8 liters mixture = 5x/8x × 8 = 5 liters
Liquid Y in 8 liters mixture = 8 - 5 = 3 liters
According to the question,
\(\frac{5x - 5}{3x - 3 + 8} = \frac{2}{3}\)
⇒ 15x - 15 = 6x - 6 + 16
⇒ 15x - 15 = 6x + 10
⇒ 15x - 6x = 10 + 15
⇒ 9x = 25
⇒ x = 25/9
Thus, the initial quantity of liquid X
⇒ 5x = 5 × 25/9 = 125/9 = 13 \(\frac{8}{9}\) liters
The correct answer is option 3.
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