Question
Download Solution PDFA vessel is filled with liquid, 5 parts of which are water and 11 parts syrup. What part of the mixture must be drawn off and replaced with water so that the mixture may be syrup and water in the ratio 3 ∶ 2?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
A vessel is filled with liquid, 5 parts of which are water and 11 parts syrup.
Explanation:
Let initially the mixture be 80 litres.
Water = 80 × 5/16 = 25 litres
Syrup = 80 × 11/16 = 55 litres
Let the mixture be drawn be 16x
According to the question,
After replacement, the quantity of water and syrup same,
(25 - 5x + 16x)/(55 - 11x) = 2/3
⇒ 75 + 33x = 110 - 22x
⇒ 55x = 35
⇒ x = 7/11
⇒ 16x → 7/11 × 16 = 112/11
⇒ (112/11)/80
= 7/55
The answer is 7/55.
Shortcut Trick
⇒ Mixture replaced = 7/(22 + 33) = 7/55
The answer is 7/55.
Last updated on Jul 10, 2025
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