Question

If \(65.7402 = 6\times A + \frac{5}{8} + 7\times C + \frac{4}{D} + 2\times E\), then the value of\(2\times A + \frac{B}{5} + 10\times C + \frac{D}{20} + 4\times E\)is

• A. 21.3006
• B. 26.2004
• C. 28.5007
• D. 23.7005

Answer 1

The Correct Option is B

Finding the Value of the Given Expression 

Step 1: Break Down the Number into Place-Value Chunks

The given number is \( 65.7402 \), which breaks down into:

• \( 6A \) contributes “60” → \( 6A = 60 \Rightarrow A = 10 \)
• \( \frac{5}{B} \) contributes “5” → \( \frac{5}{B} = 5 \Rightarrow B = 1 \)
• \( 7C \) contributes “0.7” → \( 7C = 0.7 \Rightarrow C = 0.1 \)
• \( \frac{4}{D} \) contributes “0.04” → \( \frac{4}{D} = 0.04 \Rightarrow D = 100 \)
• \( 2E \) contributes “0.0002” → \( 2E = 0.0002 \Rightarrow E = 0.0001 \)

Step 2: Compute the Desired Expression

The required expression is:

\[ 2A + \frac{B}{5} + 10C + \frac{D}{20} + 4E \]

Substituting the values of \( A, B, C, D, E \):

\[ 2(10) + \frac{1}{5} + 10(0.1) + \frac{100}{20} + 4(0.0001) \]

Computing each term:

• \( 2(10) = 20 \)
• \( \frac{1}{5} = 0.2 \)
• \( 10(0.1) = 1 \)
• \( \frac{100}{20} = 5 \)
• \( 4(0.0001) = 0.0004 \)

Step 3: Sum the Values

\[ 20 + 0.2 + 1 + 5 + 0.0004 = 26.2004 \]

Final Answer:

Thus, the correct answer is (B) 26.2004.