Read the information given below carefully and answer the question that follows:

(A) The mean of 20 observations is 17. On checking, it was found that two observations were wrongly copied as 3 and 6. If the wrong observations are replaced by correct values 8 and 9, then the correct mean will be 16.4.

(B) The ratio of $4^{3.5} : 2^5$ is same as 4 : 1

(C) The ratio of 1.5 : 2.5 can also be written as 3 : 5

(D) If : 2A = 3B = 4C, then, A : B : C is equal to 6 : 4 : 3

Choose the correct option:

Statement (A): Mean of 20 observations is 17. Wrong values: 3 and 6. Correct values: 8 and 9. Claims correct mean = 16.4.

Wrong sum $= 17 \times 20 = 340$

Correct sum $= 340 - 3 - 6 + 8 + 9$

$= 340 - 9 + 17$

$= 348$

Correct mean $= \dfrac{348}{20} = 17.4$

Statement (A) is incorrect (claims 16.4, but answer is 17.4)

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Statement (B): Ratio of $4^{3.5} : 2^5$ should be 4 : 1

Converting to base 2:

$4^{3.5} = (2^2)^{3.5}$

$= 2^{2 \times 3.5}$

$= 2^7$

$= 128$

Also, $2^5 = 32$

The ratio: $128 : 32 = 4 : 1$

Statement (B) is correct

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Statement (C): 1.5 : 2.5 = 3 : 5

Multiplying both sides by 2:

$1.5 \times 2 = 3$

$2.5 \times 2 = 5$

Therefore, $1.5 : 2.5 = 3 : 5$

Statement (C) is correct

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Statement (D): $2A = 3B = 4C$, find $A : B : C$

Let $2A = 3B = 4C = k$

From $2A = k$: $A = \dfrac{k}{2}$

From $3B = k$: $B = \dfrac{k}{3}$

From $4C = k$: $C = \dfrac{k}{4}$

The ratio: $A : B : C = \dfrac{k}{2} : \dfrac{k}{3} : \dfrac{k}{4}$

Multiplying by 12 (LCM of 2, 3, 4):

$A = \dfrac{k}{2} \times 12 = 6k$

$B = \dfrac{k}{3} \times 12 = 4k$

$C = \dfrac{k}{4} \times 12 = 3k$

Therefore, $A : B : C = 6 : 4 : 3$

Statement (D) is correct

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Summary:

(A) is incorrect

(B) is correct

(C) is correct

(D) is correct