# Q2. A mixture of paint is prepared by mixing 1 part of red pigments with 8 parts of base. In the following table, find the parts of base that need to be added.

Suppose the parts of red pigment is x and parts of base, is 'y'.

As the requirement of the number of parts of base for 1 part of red pigment is 8,

and as the parts of red pigment is increases, parts of base also increases in the same ratio. It is a case of direct proportion.

we can assume other parts of the base that will be required for red pigments as y1, y2, y3 and y4 for parts of pigment 4, 7, 12 and 20 respectively.

We make use of the relation of type

That gives for the (i) case   or   .

32 parts of the base will be required for the 4 parts of the red pigment.

(ii) If parts of red pigment used is 7 then parts of base used will be

that gives  or    .

56 parts of the base will be required for the 7 parts of the red pigment.

(iii) for 12 parts of red pigment :

we have     or   .

so, 96 parts of the base will be required for the 12 parts of the red pigment.

(iv) for 20 parts of red pigment:

we have     or  .

Hence for the following parts of red pigment, parts of base are given :

 Parts of red pigment 1 4 7 12 20 Parts of base 8 32 56 96 160

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