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Q.

In the table below, if 1 part of a red pigment requires 75 mL of base, how much red pigment should we mix with 1800 mL of base?

Part of red pigments
1
?
Base(mL)
75
1800

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a

20

b

22

c

24

d

25

answer is C.

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Detailed Solution

We have been given that 1 part of a red pigment requires 75 mL of base.
We have to find the amount of part needed for 1800 mL of base.
We know that if two quantities x and y vary in the same way while maintaining a constant ratio between their respective values, then the two quantities are said to be in direct proportion.
i.e.

x y = k,

where k is a constant positive number.
Then from the given data, we can draw the following table as,

Part of red pigments	$x 1 = 1$	$x_{2} = ?$
Base(mL)	$y_{1} = 75$	$y 2 = 1800$

Using the relation of direct proportion

x 1 y 1 = x 2 y 2

, we get,

x 1 y 1 = x 2 y 2

⇒ x 2 = x 1 y 2 y 1

⇒ x 2 = 1 × 1800 75

∴ x 2 = 24

Therefore, 24 parts of red pigment are to be mixed with 1800 mL of base.
Hence, option 3 is correct.

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