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A pot is filled with fluid, 2 parts of which are rose water and 5 parts Glycerin. What part of the mixture must be drawn off and replaced with rose water so that the mixture may be half rose water and half Glycerin?

A pot is filled with fluid, 2 parts of which are rose water and 5 parts Glycerin. What part of the mixture must be drawn off and replaced with rose water so that the mixture may be half rose water and half Glycerin? Correct Answer 3/10

Given

Part of rose water in the mixture = 2 parts

Part of Glycerin in the mixture = 5 parts

Formula used

Quantity of cheaper/Quantity of dearer = (cost price of dearer – mean price) / (mean Price - cost price of dearer)

Calculation

Suppose the pot initially contains fluid = 2 parts + 5 parts = 7 liters

Let this fluid be replaced with rose water. = x liters

Quantity of the rose water in the new mixture = 2 – (2x/7) + x

Quantity of Glycerin the in the new mixture = 5 – (5x/7)

According to question

⇒ 2 – (2x/7) + x = 5 – (5x/7)

⇒ 14 – 2x + 7x = 35 – 5x

⇒ 10x = 35 – 14

⇒ x = 21/10

 So part of the mixture replaced = (21/10) × (1/7) = 3/10

∴ The mixture is replaced with (3/10)th part.

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