Solution:

• Let the parts of red pigment mix with 1800 mL base be a

Since the red pigment is in Direct proportion with parts of the base,

So,

[tex]\quad\longrightarrow\quad \sf{\dfrac{1}{75 }mL = \dfrac{a}{1800} mL}[/tex]

[tex]\quad\longrightarrow\quad\sf{a = \dfrac{1800}{75 }}[/tex]

[tex]\quad\longrightarrow\quad\sf {a = 24}[/tex]

Answer

Hence, 24 parts of red pigment are required to mix with 1800 mL of a base to form a mixture.

[tex] \rule{300pt}{1.5pt}[/tex]

Step-by-step explanation:

[tex] \purple{ \underline{ \sf\underline{Given \: that,}}}[/tex]

1 part of red pigment requires 75 ml of base

Let x parts of red pigment require 1800 mL of base.

Parts of red pigment = 1 X

Parts of base = 75 1800

Now, as the parts of red pigment increases,

the quantity of base will also increase.

(Parts of red pigment and quantity of base are in direct proportion)

[tex] \rm \frac{1}{75 }= \frac{x}{1800} \\ \\ \rm \: \frac{1}{75 } \times 1800 = x \\ \\ \rm \: 24 = x \\ \\ \rm \purple{ x = 24}[/tex]

Therefore , 24 parts of red pigment should be mixed with 1800 mL of base.