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According to an instruction a mixture of colour and Turpentine containing half part of each is perfect for painting a wall. A painter is provided a mixture, 3 parts of which are colour and 5 parts are Turpentine. How much of the mixture drawn off and replaced with colour so that the mixture becomes perfect?

According to an instruction a mixture of colour and Turpentine containing half part of each is perfect for painting a wall. A painter is provided a mixture, 3 parts of which are colour and 5 parts are Turpentine. How much of the mixture drawn off and replaced with colour so that the mixture becomes perfect? Correct Answer 1/5<sup>th</sup> part

Let total amount of the mixture be 1 litre

3 parts of the mixture are colour and 5 parts are Turpentine

⇒ Amount of colour in the mixture = 3/8 litre

⇒ Amount of turpentine in the mixture = 5/8 litre

Let amount of mixture removed by the painter be ‘x’ litre

⇒ Amount of colour in the new mixture = (3/8 – 3x/8 + x) litre

⇒ Amount of turpentine in the new mixture = (5/8 – 5x/8) litre

The mixture will be perfect if, Amount of colour in the new mixture = Amount of turpentine in the new mixture

⇒ 3/8 – 3x/8 + x = 5/8 – 5x/8

⇒ 3 – 3x + 8x = 5 – 5x

⇒ 10x = 2

⇒ x = 1/5

∴ 1/5th part of the mixture should be replaced

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Reason R : Turpentine oil is costlier than other thinners.
Select your answer according to the coding system given below:
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