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Question
Choose the most appropriate option.
A vessel contains a mixture of milk and water in the ratio of 5:3 respectively. How much of the mixture must be siphoned off and replaced with water, so that the mixture may be half milk and half water?
Options
`1/5`
`1/4`
`1/3`
`1/7`
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Solution
`1/5`
Explanation:
Let the vessel contains 8 litres of liquid.
Let x litres of this liquid be replaced with water
Quantity of water in new mixture`=(3-(3"x")/8+"x")`litres
Quantity of milk in new mixture`=(5-(5"x")/8)`litres
`∴(3-(3"x")/8+"x")=(5-(5"x")/8)`
⇒ 5x + 24 = 40 - 5x
⇒ 10x = 16
∴`"x"=8/5`
So, part of the mixture replaced`=(8/5xx1/8)=1/5`
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